
!pip install gekko matplotlib numpy werkzeug==1.0.0

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from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt


# initialise parameters
v_max  = 30
v_min = -4
uv_max  = 2
uv_min = -2
x_s = 10
y_s = 10
x_f = 50
y_f = 40
v_bound = 0

phi_max = 0.7

# initialize GEKKO
m = GEKKO() 
nt = 101
m.time = np.linspace(0,1,nt)
obs_1 = [35, 35]
obs_2 = [35, 25]
obs_3 = [35, 30]

# Variables
x = m.Var(value=x_s)
y = m.Var(value=y_s)
v = m.Var(value=0, lb=v_min, ub=v_max)
th = m.Var(value=0, lb=-np.pi, ub=np.pi) # bound heading to -pi/2 and pi/2

# optimize final time
tf = m.FV(value=1.0,lb=0.1,ub=100.0)
tf.STATUS = 1

# control changes every time period
uv = m.MV(value=0, lb=uv_min,ub=uv_max)
uv.STATUS = 1
phi = m.MV(value=0, lb=-phi_max, ub=phi_max)
phi.STATUS = 1

# define the ODEs that describe the movement of the vehicle
m.Equation(x.dt()==v*m.cos(th)*tf)
m.Equation(y.dt()==v*m.sin(th)*tf)
m.Equation(v.dt()==uv*tf)
m.Equation(th.dt()==phi*tf)

# define path constraints
m.Equation(x >= 0)
m.Equation(y >= 0)
m.Equation((x - obs_3[0])**2 + (y - obs_3[1])**2 >= 6.5 * 6.5) # we implement the obstacles as three overlapping circular blobs
m.Equation((x - obs_2[0])**2 + (y - obs_2[1])**2 >= 6.5 * 6.5) 
m.Equation((x - obs_1[0])**2 + (y - obs_1[1])**2 >= 6.5 * 6.5)

# define boundary constraints
m.fix(x, pos=len(m.time)-1,val=x_f)
m.fix(y, pos=len(m.time)-1,val=y_f)
m.fix(v, pos=len(m.time)-1,val=0)

# Objective function
m.Obj(tf)

# Solve
m.options.IMODE = 6
m.options.MAX_ITER = 2000
m.solve(disp=True) # set to False to hide the solver logs

#Presentation of results
print('Final Time: ' + str(tf.value[0]))

apm 155.198.90.49_gk_model4 <br><pre> ----------------------------------------------------------------
 APMonitor, Version 1.0.0
 APMonitor Optimization Suite
 ----------------------------------------------------------------
 
 
 --------- APM Model Size ------------
 Each time step contains
   Objects      :            0
   Constants    :            0
   Variables    :           12
   Intermediates:            0
   Connections  :            6
   Equations    :           10
   Residuals    :           10
 
 Number of state variables:           2295
 Number of total equations: -         2100
 Number of slack variables: -          500
 ---------------------------------------
 Degrees of freedom       :           -305
 
 * Warning: DOF <= 0
 **********************************************
 Dynamic Control with Interior Point Solver
 **********************************************
  
  
 Info: Exact Hessian

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

This is Ipopt version 3.12.10, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...:     4875
Number of nonzeros in inequality constraint Jacobian.:      800
Number of nonzeros in Lagrangian Hessian.............:      796

Total number of variables............................:     2295
                     variables with only lower bounds:      900
                variables with lower and upper bounds:      400
                     variables with only upper bounds:        0
Total number of equality constraints.................:     1700
Total number of inequality constraints...............:      400
        inequality constraints with only lower bounds:      400
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.0000024e+02 1.21e+03 1.00e+02   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  9.9957784e+01 1.21e+03 1.00e+02  -5.7 1.64e+05    -  8.92e-06 4.76e-06h  1
   2r 9.9957784e+01 1.21e+03 9.99e+02   2.6 0.00e+00    -  0.00e+00 2.39e-08R  2
   3r 1.0331018e+02 1.13e+03 9.97e+02   2.4 5.86e+04    -  1.67e-04 3.03e-03f  1
   4r 4.0165492e+02 1.10e+03 9.94e+02   3.1 1.76e+04    -  4.32e-03 2.00e-03f  1
   5r 2.8372686e+02 8.58e+02 9.94e+02  -3.6 1.72e+04    -  8.98e-04 3.22e-03f  1
   6r 2.8572786e+02 8.55e+02 9.98e+02   1.8 1.17e+01   2.0 9.62e-01 4.02e-02f  1
   7r 3.2216336e+02 8.34e+02 1.01e+03   2.4 3.28e+01   1.5 3.37e-01 1.29e-01f  1
   8r 8.6142226e+01 4.39e+02 1.00e+03  -3.6 1.23e+04    -  3.98e-03 7.46e-03f  1
   9r 8.6032292e+01 4.17e+02 1.00e+03  -3.6 4.11e+03    -  9.82e-04 1.06e-03f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10r 8.6288200e+01 3.99e+02 1.00e+03   1.1 5.58e+04    -  1.34e-04 1.13e-03f  1
  11  1.1707586e+02 3.98e+02 1.02e+01  -5.5 4.41e+04    -  1.30e-03 1.15e-03h  1
  12  1.1769701e+02 3.98e+02 9.99e+01  -5.5 2.62e+05    -  7.51e-04 1.15e-05h  1
  13r 1.1769701e+02 3.98e+02 9.99e+02   2.5 0.00e+00    -  0.00e+00 5.88e-08R  2
  14r 1.2133054e+02 3.02e+02 9.90e+02  -3.6 5.45e+03    -  1.12e-02 9.37e-03f  1
  15r 1.2133054e+02 3.02e+02 9.99e+02   2.5 0.00e+00    -  0.00e+00 1.15e-07R  2
  16r 2.3223117e+02 2.13e+02 9.79e+02   2.3 5.98e+03    -  1.02e-01 1.95e-02f  1
  17  2.7544861e+02 2.13e+02 2.27e+02  -5.8 7.04e+04    -  1.34e-03 2.65e-04h  1
  18  3.3006190e+02 2.13e+02 7.77e+02   0.7 2.07e+06    -  4.78e-05 9.37e-06h  2
  19  3.8430506e+02 2.13e+02 6.27e+02  -1.3 3.60e+06    -  4.17e-05 6.95e-06h  4
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20  4.4669538e+02 2.13e+02 4.24e+02  -1.9 2.76e+06    -  6.33e-05 8.72e-06h  4
  21  4.9644979e+02 2.13e+02 3.29e+02  -5.8 1.48e+06    -  6.21e-05 7.14e-06h  5
  22  5.3252740e+02 2.13e+02 2.64e+02  -5.8 9.45e+05    -  7.13e-05 5.26e-06h  6
  23  5.8044898e+02 2.13e+02 1.00e+02  -5.8 6.87e+05    -  3.13e-04 7.02e-06h  6
  24  4.3534948e+03 2.13e+02 1.68e+03   2.2 3.12e+05    -  3.60e-04 5.54e-04f  1
  25  4.3971753e+03 2.13e+02 1.68e+03   0.1 1.59e+05  -2.0 5.54e-05 1.18e-05h  1
  26  5.1009823e+03 2.13e+02 1.65e+03   0.1 2.95e+05  -2.5 2.45e-05 9.65e-05h  1
  27r 5.1009823e+03 2.13e+02 9.99e+02   2.3 0.00e+00  -1.1 0.00e+00 5.00e-07R  4
  28r 5.0525450e+03 2.13e+02 9.99e+02  -3.8 1.39e+04    -  4.84e-03 9.08e-05f  1
  29r 4.8897574e+03 7.77e+01 9.99e+02  -3.8 1.60e+05    -  3.93e-05 1.31e-03f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  30r 4.8897574e+03 7.77e+01 9.99e+02   1.7 0.00e+00    -  0.00e+00 4.61e-07R  3
  31r 3.4797404e+03 7.34e+01 1.55e+03   2.2 2.09e+04    -  5.17e-03 1.43e-03f  1
  32  3.4014524e+03 7.33e+01 9.95e+01   0.1 1.61e+04    -  7.39e-03 5.60e-04f  1
  33  3.4981901e+03 7.33e+01 9.95e+01   0.1 4.31e+05    -  4.88e-05 4.63e-05h  1
  34  3.8077821e+03 7.33e+01 9.96e+01   0.1 3.29e+05    -  1.25e-04 8.51e-05h  1
  35  5.2966177e+03 7.33e+01 3.21e+02   0.1 2.07e+05    -  3.28e-04 2.95e-04h  1
  36r 5.2966177e+03 7.33e+01 9.99e+02   1.4 0.00e+00    -  0.00e+00 3.93e-07R  4
  37r 4.2191998e+03 6.96e+01 9.96e+02   3.3 1.28e+04    -  1.06e-02 1.89e-03f  1
  38r 3.8730788e+03 5.65e+01 9.88e+02   2.5 6.99e+02    -  2.88e-02 7.74e-03f  1
  39  3.9244683e+03 5.65e+01 3.06e+02  -5.2 1.98e+04    -  7.06e-03 9.55e-05h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  40  5.4924166e+03 5.65e+01 7.57e+02  -5.2 3.97e+04    -  1.32e-03 5.33e-04h  1
  41r 5.4924166e+03 5.65e+01 1.00e+03   1.3 0.00e+00    -  0.00e+00 3.57e-07R  5
  42r 5.5827278e+03 5.29e+01 9.94e+02   3.2 3.34e+03    -  2.17e-02 3.96e-03f  1
  43r 5.5369033e+03 3.31e+01 9.58e+02   2.8 1.35e+02    -  2.48e-01 3.04e-02f  1
  44r 6.2781865e+03 2.99e+01 7.45e+02   2.4 8.70e+01    -  2.79e-01 2.22e-01f  1
  45r 6.3982475e+03 2.83e+01 6.16e+02   2.1 6.27e+01    -  3.03e-01 1.74e-01f  1
  46r 6.5283263e+03 2.13e+01 5.82e+02   0.9 4.22e+01    -  9.88e-02 2.11e-01f  1
  47r 6.8292800e+03 2.11e+01 5.18e+02   1.6 7.72e+01    -  1.32e-01 1.30e-01f  1
  48r 7.1050612e+03 2.07e+01 5.93e+02   2.2 2.33e+01    -  5.68e-01 2.04e-01f  1
  49r 7.1620350e+03 2.04e+01 2.70e+02   1.2 7.96e+00    -  5.01e-01 6.24e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  50r 8.1347251e+03 2.06e+01 2.26e+02   1.2 5.68e+01    -  3.65e-01 1.71e-01f  1
  51r 8.5820225e+03 2.07e+01 3.22e+02   0.7 5.84e+01    -  2.22e-01 7.66e-02f  1
  52r 9.9859716e+03 2.07e+01 2.15e+02  -4.4 1.49e+03  -2.0 7.74e-03 1.49e-02f  1
  53r 9.9726618e+03 2.09e+01 9.04e+02   1.5 4.45e+01   0.2 6.53e-01 5.80e-02f  1
  54r 9.8476841e+03 2.11e+01 8.59e+01   1.4 1.74e+01    -  8.71e-01 1.00e+00f  1
  55r 9.9711316e+03 2.12e+01 1.01e+02  -0.0 4.50e+00    -  9.26e-01 8.49e-01f  1
  56r 9.9780731e+03 2.15e+01 2.08e+02  -5.3 3.55e+01  -0.2 1.43e-01 1.04e-01f  1
  57r 9.9765975e+03 2.15e+01 3.44e+02   0.6 2.19e+00   1.1 4.54e-01 2.28e-01f  1
  58r 9.9771585e+03 2.15e+01 9.41e+01   0.5 3.37e+00   0.6 8.73e-01 7.75e-01f  1
  59r 9.9819235e+03 2.15e+01 9.74e+01   0.3 4.16e+01    -  2.89e-01 1.86e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  60r 9.8989274e+03 4.38e+01 3.24e+03   2.5 6.77e+02    -  1.11e-02 5.27e-02f  1
  61r 9.9380525e+03 4.31e+01 3.16e+03   1.1 5.76e+01   0.1 4.78e-02 1.59e-02f  1
  62r 9.9250201e+03 3.32e+01 2.39e+03   1.1 8.45e+00   0.6 2.73e-01 2.29e-01f  1
  63r 9.9173152e+03 2.45e+01 1.81e+03   1.1 4.09e+00   1.0 5.74e-01 2.62e-01f  1
  64r 9.9284020e+03 2.13e+01 1.04e+03   1.1 2.21e+00   1.4 2.19e-01 5.04e-01f  1
  65r 9.9266463e+03 2.13e+01 9.88e+02   1.1 3.45e+01    -  1.00e+00 5.33e-02f  1
  66r 9.9174161e+03 2.13e+01 8.36e+02   1.1 2.66e+01    -  1.00e+00 2.95e-01f  1
  67r 9.9021038e+03 2.14e+01 6.13e+02   1.1 1.60e+01    -  1.00e+00 1.00e+00h  1
  68r 9.9575308e+03 2.14e+01 3.71e+02   0.4 8.86e+00    -  2.78e-01 5.55e-01f  1
  69r 9.9704585e+03 2.15e+01 3.49e+02   0.4 4.97e+01    -  2.01e-01 1.78e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  70r 9.9744896e+03 2.15e+01 4.00e+02   0.4 3.38e+01    -  4.55e-01 1.42e-01f  1
  71r 9.9808407e+03 2.15e+01 3.61e+02   0.4 2.94e+01    -  4.99e-01 3.27e-01f  1
  72r 9.9858060e+03 2.15e+01 2.21e+02   0.4 2.14e+01    -  7.19e-01 4.54e-01f  1
  73r 9.9899244e+03 2.14e+01 1.75e+02   0.4 1.22e+01    -  1.00e+00 7.99e-01f  1
  74r 9.9951267e+03 2.14e+01 1.96e+02  -0.4 2.65e+00    -  9.91e-01 5.91e-01f  1
  75r 9.9968070e+03 2.14e+01 1.11e+02  -5.9 1.52e+00   0.9 4.02e-01 3.02e-01f  1
  76r 9.9971110e+03 2.14e+01 1.76e+02  -0.2 7.32e+00   0.5 2.32e-01 1.73e-01f  1
  77r 9.9972816e+03 2.14e+01 6.44e+02  -0.4 4.25e+02    -  2.64e-02 1.30e-02f  1
  78r 9.9972520e+03 2.13e+01 1.39e+03   1.0 6.99e+02    -  2.99e-02 6.97e-03f  1
  79r 9.9972339e+03 2.13e+01 1.15e+03  -0.1 3.98e+01    -  1.59e-01 3.58e-02h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  80r 9.9973614e+03 2.13e+01 1.18e+03  -0.1 5.75e+01    -  8.12e-02 5.22e-02f  1
  81r 9.9974362e+03 2.12e+01 1.04e+03  -0.1 5.47e+01    -  6.56e-01 3.36e-02f  1
  82r 9.9977748e+03 2.11e+01 9.50e+02  -0.1 5.30e+01    -  1.22e-01 2.48e-01f  1
  83r 9.9978083e+03 2.10e+01 8.07e+02  -0.1 4.14e+01    -  3.23e-01 4.10e-02f  1
  84r 9.9981643e+03 2.10e+01 2.62e+02  -0.1 3.98e+01    -  1.00e+00 5.32e-01f  1
  85r 9.9994606e+03 2.10e+01 6.08e+01  -0.9 1.96e+01    -  1.00e+00 8.02e-01f  1
  86r 9.9994889e+03 2.10e+01 3.99e+02  -0.6 9.43e+00  -0.0 8.45e-01 3.58e-01f  1
  87r 9.9997782e+03 2.10e+01 4.83e+01  -0.8 1.69e+01  -0.5 1.00e+00 1.00e+00f  1
  88r 9.9998941e+03 2.10e+01 1.18e+02  -1.5 8.00e+00  -0.1 9.99e-01 4.82e-01f  1
  89r 9.9999302e+03 2.10e+01 1.46e+02  -1.4 3.35e+01  -0.6 3.70e-01 3.22e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  90r 9.9999280e+03 2.10e+01 4.64e+02  -0.9 1.41e+01  -0.1 9.32e-01 2.52e-02f  1
  91r 9.9999379e+03 2.10e+01 2.69e+02  -1.1 2.35e+01  -0.6 3.94e-01 4.62e-01f  1
  92r 9.9988600e+03 2.10e+01 4.01e+03  -0.2 5.91e+01  -1.1 4.56e-02 8.85e-01f  1
  93r 9.9989077e+03 2.10e+01 3.52e+03  -0.4 9.34e+00   0.2 2.49e-01 7.37e-02f  1
  94r 9.9990116e+03 2.10e+01 2.73e+03  -0.4 6.71e+00   0.7 2.38e-01 2.27e-01f  1
  95r 9.9991439e+03 2.10e+01 1.92e+03  -0.4 7.31e+00   0.2 6.58e-02 2.67e-01f  1
  96r 9.9991781e+03 2.10e+01 1.69e+03  -0.4 5.85e+00   0.6 6.38e-02 9.58e-02f  1
  97r 9.9992033e+03 2.10e+01 1.54e+03  -0.4 2.56e+00   1.0 7.67e-02 8.96e-02h  1
  98r 9.9992321e+03 2.10e+01 1.40e+03  -0.4 3.89e+00   0.6 9.41e-02 9.32e-02h  1
  99r 9.9993107e+03 2.10e+01 1.05e+03  -0.4 2.23e+00   1.0 3.72e-02 3.01e-01h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 100r 9.9993281e+03 2.10e+01 9.84e+02  -0.4 4.05e+00   0.5 4.41e-02 5.75e-02f  1
 101r 9.9993877e+03 2.10e+01 8.64e+02  -0.4 1.67e+00   0.9 7.66e-02 2.90e-01h  1
 102r 9.9994053e+03 2.10e+01 7.12e+02  -0.4 4.28e+00   0.5 2.05e-01 1.39e-01f  1
 103r 9.9994507e+03 2.10e+01 4.94e+02  -0.4 1.77e+00   0.9 2.30e-01 4.40e-01h  1
 104r 9.9994568e+03 2.10e+01 4.40e+02  -0.4 4.40e+00   0.4 2.92e-01 1.48e-01f  1
 105r 9.9994669e+03 2.10e+01 2.85e+02  -0.4 1.81e+00   0.8 4.46e-01 2.80e-01f  1
 106r 9.9994689e+03 2.10e+01 3.69e+02  -0.4 4.55e+00   0.4 4.80e-01 1.01e-01f  1
 107r 9.9994843e+03 2.10e+01 8.67e+01  -0.4 1.91e+00   0.8 1.00e+00 7.71e-01f  1
 108r 9.9994838e+03 2.10e+01 9.94e+01  -0.4 4.43e+00   0.3 2.59e-01 2.09e-01f  1
 109r 9.9994834e+03 2.10e+01 2.46e+02  -0.4 1.26e+01  -0.2 6.33e-02 1.33e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 110r 9.9994843e+03 2.10e+01 3.49e+02  -0.4 3.63e+00   0.3 6.25e-01 2.46e-01f  1
 111r 9.9994843e+03 2.10e+01 4.16e+02  -0.4 7.77e+00  -0.2 3.30e-01 1.12e-01f  1
 112r 9.9994765e+03 2.10e+01 3.23e+02  -0.4 1.77e+01  -0.7 2.21e-01 3.11e-01h  1
 113r 9.9994701e+03 2.10e+01 2.66e+02  -0.4 4.52e+01    -  1.31e-01 5.57e-02h  4
 114r 9.9994681e+03 2.10e+01 6.97e+02  -0.4 7.20e+00  -0.3 6.83e-01 1.52e-01h  1
 115r 9.9994617e+03 2.10e+01 5.17e+02  -0.4 4.13e+01    -  1.45e-01 6.09e-02h  4
 116r 9.9994492e+03 2.10e+01 2.52e+02  -0.4 1.47e+01  -0.7 3.96e-01 3.26e-01h  1
 117r 9.9994397e+03 2.10e+01 1.45e+02  -0.4 6.32e+00  -0.3 7.63e-01 5.70e-01h  1
 118r 9.9994367e+03 2.10e+01 2.79e+02  -0.4 1.23e+01  -0.8 4.82e-01 8.85e-02h  4
 119r 9.9994267e+03 2.10e+01 1.24e+02  -0.4 5.94e+00  -0.4 6.86e-01 5.91e-01H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 120r 9.9996814e+03 2.10e+01 1.76e+02  -6.4 1.11e+01  -0.8 3.48e-01 3.92e-01f  1
 121r 9.9996331e+03 2.10e+01 3.95e+02  -0.4 4.54e+00   0.5 3.43e-01 1.28e-01f  1
 122r 9.9996372e+03 2.10e+01 6.65e+02  -0.7 2.84e+01    -  1.00e+00 2.01e-01h  1
 123r 9.9996433e+03 2.10e+01 5.32e+02  -0.7 2.38e+01    -  2.06e-01 1.01e-01f  1
 124r 9.9996795e+03 2.10e+01 2.76e+02  -0.7 2.14e+01    -  3.54e-01 5.43e-01f  1
 125r 9.9996927e+03 2.10e+01 9.75e+01  -0.7 1.09e+01    -  6.68e-01 6.45e-01f  1
 126r 9.9996935e+03 2.10e+01 3.64e+02  -0.7 2.18e+01    -  8.96e-01 9.64e-02f  1
 127r 9.9997000e+03 2.10e+01 1.10e+03  -0.7 3.27e+00    -  1.51e-01 1.00e+00f  1
 128r 9.9997024e+03 2.10e+01 4.85e+02  -0.7 2.83e+00    -  1.00e+00 1.00e+00h  1
 129r 9.9997013e+03 2.10e+01 1.08e+01  -0.7 7.40e-01    -  1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 130r 9.9999507e+03 2.10e+01 2.54e+01  -2.5 7.65e-01    -  9.85e-01 6.72e-01f  1
 131r 9.9999615e+03 2.10e+01 2.41e+02  -2.0 1.11e+01   0.0 3.52e-01 1.03e-01f  1
 132r 9.9999362e+03 2.10e+01 1.96e+02  -0.8 2.72e+01  -0.5 1.62e-01 1.57e-01f  1
 133r 9.9999728e+03 2.10e+01 1.09e+02  -1.3 2.21e+01    -  1.00e+00 6.01e-01f  1
 134r 9.9999875e+03 2.10e+01 6.55e+01  -1.3 1.14e+02    -  1.62e-01 2.48e-01f  1
 135r 9.9999925e+03 2.10e+01 6.01e+01  -1.3 9.10e+01    -  1.90e-01 1.28e-01f  1
 136r 1.0000012e+04 2.10e+01 8.94e+01  -1.3 7.92e+01    -  8.33e-01 7.12e-01f  1
 137r 1.0000060e+04 2.10e+01 1.73e+01  -2.3 2.53e+01    -  9.98e-01 8.12e-01f  1
 138r 1.0000065e+04 2.10e+01 5.99e+01  -7.9 6.33e+01  -0.9 3.07e-02 2.70e-01f  1
 139r 1.0000064e+04 2.10e+01 1.09e+02  -1.8 3.97e+01  -0.5 1.25e-01 3.18e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 140r 1.0000065e+04 2.10e+01 6.00e+01  -2.1 1.45e+02    -  2.98e-03 6.46e-02f  1
 141r 1.0000065e+04 2.11e+01 7.34e+01  -2.1 1.62e+03    -  1.66e-04 3.46e-03f  1
 142r 1.0000066e+04 2.12e+01 8.40e+01  -2.1 5.54e+01  -1.0 8.46e-02 1.29e-01f  1
 143r 1.0000066e+04 2.13e+01 2.15e+02  -2.1 1.14e+02  -1.5 6.58e-04 7.87e-02f  1
 144r 1.0000067e+04 2.13e+01 2.33e+02  -2.1 5.72e+01  -1.0 2.14e-01 6.70e-02f  1
 145r 1.0000067e+04 2.16e+01 1.74e+02  -2.1 2.09e+02  -1.5 1.12e-03 1.00e-01f  1
 146r 1.0000067e+04 2.16e+01 1.89e+02  -3.7 5.90e+01  -1.1 1.64e-01 2.66e-03f  1
 147r 1.0000053e+04 2.16e+01 1.42e+02  -0.8 4.96e+01  -0.7 5.38e-02 9.45e-02f  1
 148r 1.0000053e+04 2.16e+01 5.18e+02  -1.8 1.76e+02    -  3.68e-02 3.75e-03h  1
 149r 1.0000056e+04 2.16e+01 5.17e+02  -1.8 1.12e+02    -  5.79e-03 1.69e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 150r 1.0000056e+04 2.16e+01 6.63e+02  -2.2 9.56e+01    -  2.09e-01 1.76e-03f  1
 151r 1.0000059e+04 2.16e+01 3.78e+02  -7.7 7.09e+01  -1.1 1.59e-03 8.74e-02f  1
 152r 1.0000059e+04 2.16e+01 3.78e+02  -1.1 2.66e+02  -0.7 8.78e-02 6.82e-04h  1
 153r 1.0000059e+04 2.16e+01 3.73e+02  -1.8 7.99e+01  -1.2 6.22e-02 1.36e-02h  1
 154r 1.0000067e+04 2.15e+01 1.51e+03  -2.5 9.83e+01    -  9.82e-04 3.96e-01f  1
 155r 1.0000045e+04 2.14e+01 1.46e+03   0.2 6.86e+02  -0.8 1.63e-02 1.50e-02F  1
 156r 1.0000044e+04 2.15e+01 1.41e+03  -1.5 3.95e+02    -  3.06e-02 3.04e-02h  1
 157r 1.0000050e+04 2.14e+01 3.77e+02  -1.5 6.49e+00  -0.3 2.88e-01 1.00e+00f  1
 158r 9.9999868e+03 2.15e+01 1.75e+02  -0.8 1.69e+01  -0.8 6.30e-01 5.64e-01f  1
 159r 9.9999867e+03 2.15e+01 1.74e+02  -1.1 1.31e+02  -1.3 7.23e-02 1.45e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 160r 9.9999864e+03 2.15e+01 1.70e+02  -1.1 1.57e+02    -  3.21e-03 2.77e-02f  2
 161r 9.9999861e+03 2.15e+01 1.67e+02  -1.1 1.53e+02    -  2.39e-01 2.61e-02f  4
 162r 9.9999858e+03 2.15e+01 1.71e+02  -1.1 1.49e+02    -  4.26e-02 2.18e-02h  5
 163r 9.9999852e+03 2.15e+01 2.57e+02  -1.1 1.45e+02    -  2.12e-01 4.48e-02h  4
 164r 9.9999849e+03 2.15e+01 3.03e+02  -1.1 1.39e+02    -  1.52e-01 2.69e-02h  5
 165r 9.9999845e+03 2.15e+01 3.45e+02  -1.1 1.34e+02    -  1.78e-01 3.08e-02h  5
 166r 9.9999840e+03 2.15e+01 4.98e+02  -1.1 1.30e+02    -  6.26e-01 3.54e-02h  5
 167r 9.9999834e+03 2.15e+01 4.98e+02  -1.1 1.25e+02    -  2.49e-01 4.07e-02h  5
 168r 9.9999829e+03 2.15e+01 5.40e+02  -1.1 1.20e+02    -  1.00e+00 3.89e-02h  5
 169r 9.9999824e+03 2.15e+01 5.18e+02  -1.1 1.15e+02    -  3.07e-01 3.76e-02h  5
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 170r 9.9999744e+03 2.14e+01 3.93e+02  -1.1 1.10e+02    -  1.00e+00 5.79e-01w  1
 171r 9.9999741e+03 2.13e+01 3.77e+02  -1.1 4.37e+01    -  4.51e-01 4.26e-02w  1
 172r 9.9999732e+03 2.12e+01 3.19e+02  -1.1 4.18e+01    -  2.41e-01 1.78e-01w  1
 173r 9.9999814e+03 2.15e+01 4.71e+02  -1.1 3.41e+01    -  1.00e+00 7.24e-02h  3
 174r 9.9999805e+03 2.15e+01 4.36e+02  -1.1 1.02e+02    -  3.98e-01 6.81e-02h  4
 175r 9.9999801e+03 2.15e+01 4.09e+02  -1.1 9.47e+01    -  1.00e+00 3.17e-02h  5
 176r 9.9999797e+03 2.14e+01 3.93e+02  -1.1 9.15e+01    -  5.15e-01 3.34e-02h  5
 177r 9.9999793e+03 2.14e+01 3.71e+02  -1.1 8.83e+01    -  1.00e+00 3.49e-02h  5
 178r 9.9999789e+03 2.14e+01 3.53e+02  -1.1 8.51e+01    -  5.99e-01 3.56e-02h  5
 179r 9.9999785e+03 2.14e+01 3.31e+02  -1.1 8.19e+01    -  6.31e-01 3.52e-02h  5
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 180r 9.9999782e+03 2.14e+01 3.10e+02  -1.1 7.89e+01    -  4.61e-01 3.49e-02h  5
 181r 9.9999779e+03 2.14e+01 2.82e+02  -1.1 7.60e+01    -  5.47e-01 3.49e-02h  5
 182r 9.9999776e+03 2.13e+01 2.69e+02  -1.1 7.32e+01    -  6.07e-01 3.53e-02h  5
 183r 9.9999729e+03 2.11e+01 2.17e+02  -1.1 7.05e+01    -  4.61e-01 5.84e-01w  1
 184r 9.9999726e+03 2.11e+01 1.77e+02  -1.1 2.80e+01    -  1.00e+00 2.63e-01w  1
 185r 9.9999720e+03 2.10e+01 5.29e+01  -1.1 2.05e+01    -  1.00e+00 7.21e-01w  1
 186r 9.9999718e+03 2.10e+01 3.64e+00  -1.1 5.55e+00    -  1.00e+00 1.00e+00h  1
 187r 1.0000040e+04 2.10e+01 2.34e+01  -3.0 5.29e-01    -  9.96e-01 6.61e-01f  1
 188r 9.9999954e+03 2.10e+01 3.24e+01  -0.6 7.91e+01  -0.9 2.30e-01 1.43e-01f  1
 189r 9.9999954e+03 2.10e+01 6.94e+01  -1.3 1.22e+02    -  1.17e-01 4.53e-03h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 190r 1.0000025e+04 2.10e+01 3.63e+01  -1.3 4.62e+01    -  3.20e-01 1.00e+00f  1
 191r 1.0000022e+04 2.10e+01 3.12e+01  -1.3 1.07e+00    -  4.79e-01 1.00e+00h  1
 192r 1.0000065e+04 2.10e+01 1.10e+01  -7.3 4.57e-01    -  6.37e-01 7.62e-01f  1
 193r 1.0000065e+04 2.10e+01 1.27e+02  -1.9 3.39e+01  -0.5 1.18e-01 2.87e-02f  1
 194r 1.0000065e+04 2.10e+01 7.58e+01  -1.9 2.17e+02    -  2.04e-03 4.88e-02f  1
 195r 1.0000065e+04 2.11e+01 8.68e+01  -1.9 2.12e+02    -  2.68e-03 2.40e-02f  1
 196r 1.0000066e+04 2.12e+01 8.59e+01  -1.9 3.06e+02    -  1.82e-02 1.88e-02f  1
 197r 1.0000066e+04 2.16e+01 1.55e+02  -1.9 9.24e+02    -  1.11e-02 2.62e-02f  1
 198r 1.0000066e+04 2.16e+01 1.49e+02  -1.9 3.91e+01  -0.9 9.62e-02 1.73e-01f  1
 199r 1.0000066e+04 2.16e+01 1.46e+02  -1.9 8.20e+01  -1.4 4.46e-03 9.08e-04f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 200r 1.0000066e+04 2.16e+01 1.62e+02  -1.9 3.19e+02    -  6.66e-02 2.46e-03f  1
 201r 1.0000066e+04 2.16e+01 2.35e+02  -1.9 3.21e+02    -  6.56e-03 2.09e-02f  1
 202r 1.0000067e+04 2.16e+01 9.23e+02  -1.9 3.71e+02    -  8.60e-03 1.86e-02f  1
 203r 1.0000066e+04 2.16e+01 7.00e+02  -1.9 7.19e+00  -0.1 2.35e-01 2.40e-01f  1
 204r 1.0000066e+04 2.16e+01 1.25e+03  -1.9 1.29e+03    -  6.37e-03 1.43e-03f  1
 205r 1.0000066e+04 2.16e+01 7.57e+02  -1.9 1.42e+03    -  7.23e-04 4.73e-03f  1
 206r 1.0000066e+04 2.15e+01 4.50e+02  -1.9 1.68e+01  -0.6 7.63e-03 3.17e-01f  1
 207r 1.0000066e+04 2.15e+01 5.14e+02  -1.9 6.69e+01  -1.0 1.01e-01 1.16e-03f  1
 208r 1.0000066e+04 2.14e+01 6.20e+02  -1.9 1.83e+01  -0.6 2.58e-01 7.60e-01f  1
 209r 1.0000067e+04 2.13e+01 5.79e+02  -7.9 1.34e+02  -1.1 7.09e-02 4.17e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 210r 1.0000066e+04 2.11e+01 3.71e+02  -1.7 1.56e+02  -0.7 1.63e-02 1.11e-01f  1
 211r 1.0000066e+04 2.11e+01 3.65e+02  -2.0 1.85e+01  -1.1 4.73e-01 1.50e-02f  1
 212r 1.0000068e+04 2.07e+01 2.99e+02  -2.0 3.82e+01  -0.7 1.57e-01 5.07e-01f  1
 213r 1.0000068e+04 2.05e+01 3.05e+02  -2.0 6.18e+02  -1.2 8.86e-04 8.48e-03f  1
 214r 1.0000068e+04 2.05e+01 3.30e+02  -2.0 5.28e+01  -0.8 3.46e-01 1.31e-03f  1
 215r 1.0000069e+04 1.99e+01 3.29e+02  -2.0 3.11e+02  -1.2 1.20e-02 5.29e-02f  1
 216r 1.0000069e+04 1.95e+01 2.76e+02  -2.0 5.51e+01  -0.8 1.45e-01 1.56e-01f  1
 217r 1.0000069e+04 1.95e+01 9.99e+02   1.3 0.00e+00    -  0.00e+00 3.52e-07R  2
 218r 1.0000058e+04 1.94e+01 9.96e+02  -0.8 2.83e+03    -  2.48e-03 2.63e-03f  1
 219r 9.9968029e+03 1.92e+01 9.95e+02   1.5 1.20e+04    -  1.86e-04 3.39e-03f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 220r 9.9956297e+03 1.92e+01 1.40e+03   1.1 4.31e+02    -  4.81e-01 5.92e-03f  1
 221r 9.9957493e+03 1.92e+01 9.45e+02   0.5 6.66e+02    -  3.89e-01 4.33e-02f  1
 222r 9.9934910e+03 2.30e+01 7.59e+02   1.2 8.38e+02    -  9.59e-02 1.96e-01f  1
 223r 9.9830879e+03 1.92e+01 5.66e+02   1.7 1.58e+02    -  2.90e-01 2.55e-01f  1
 224r 9.9865937e+03 1.91e+01 2.61e+02   1.3 3.06e+01    -  1.00e+00 6.81e-01f  1
 225r 9.9900933e+03 1.91e+01 1.78e+02   0.6 6.58e+01    -  8.62e-01 3.13e-01f  1
 226r 9.9916899e+03 1.91e+01 2.09e+02   0.3 7.83e+01    -  7.06e-01 2.37e-01f  1
 227r 9.9957962e+03 1.91e+01 2.82e+02   0.5 7.96e+01    -  9.43e-01 8.71e-01f  1
 228r 9.9989095e+03 1.91e+01 1.10e+01   0.2 1.72e+01    -  9.01e-01 1.00e+00f  1
 229r 9.9999160e+03 1.92e+01 1.02e+01  -5.7 3.00e+01    -  7.83e-01 8.80e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 230r 9.9999563e+03 1.92e+01 2.64e+02  -1.4 3.60e+00   0.0 9.29e-01 3.08e-01f  1
 231r 9.9999198e+03 1.92e+01 1.05e+03   0.8 5.68e+02    -  6.00e-01 7.57e-03f  1
 232r 9.9986686e+03 1.92e+01 1.67e+03   0.1 4.46e+01    -  1.15e-01 1.00e+00f  1
 233r 9.9989393e+03 1.91e+01 8.15e+02   0.1 4.42e+00  -0.5 8.49e-01 4.18e-01f  1
 234r 9.9635214e+03 1.91e+01 1.54e+03   2.1 1.67e+02    -  6.65e-02 3.25e-01f  1
 235r 9.9712829e+03 1.93e+01 9.69e+02   1.5 9.94e+01    -  2.82e-01 3.56e-01f  1
 236r 9.9920139e+03 1.92e+01 6.20e+02   0.8 4.04e+01    -  6.43e-01 7.21e-01f  1
 237r 9.9931493e+03 1.92e+01 3.63e+02   0.8 2.71e+01    -  6.23e-01 3.93e-01f  1
 238r 9.9950255e+03 1.91e+01 7.56e+01   0.8 1.40e+01    -  6.26e-01 1.00e+00f  1
 239r 9.9990995e+03 1.92e+01 5.03e+00   0.1 1.99e+00    -  1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 240r 9.9997302e+03 1.92e+01 9.43e+01  -1.3 7.97e+01    -  4.59e-01 7.66e-01f  1
 241r 9.9997298e+03 1.92e+01 2.98e+02  -0.4 3.90e+02    -  3.61e-01 2.03e-03f  1
 242r 9.9996669e+03 1.92e+01 1.00e+02  -0.4 8.31e+01    -  6.50e-01 6.58e-01f  1
 243r 9.9996446e+03 1.91e+01 6.95e+00  -0.4 2.95e+01    -  1.00e+00 9.90e-01f  1
 244r 1.0000074e+04 1.92e+01 4.19e+00  -2.0 9.26e-01    -  9.97e-01 9.99e-01f  1
 245r 1.0000066e+04 1.92e+01 5.59e+02  -0.9 8.85e+02    -  3.13e-01 9.11e-02f  1
 246r 1.0000067e+04 1.92e+01 5.52e+02  -7.5 6.63e+01    -  2.90e-02 1.36e-02f  1
 247r 1.0000067e+04 1.92e+01 4.26e+02  -2.3 2.30e+00  -0.1 1.00e+00 6.09e-03f  1
 248r 1.0000067e+04 1.92e+01 3.78e+02  -7.8 4.78e+02    -  5.35e-02 9.52e-02f  1
 249r 1.0000050e+04 1.88e+01 5.44e+02  -1.5 7.35e+00  -0.5 1.97e-01 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 250r 1.0000065e+04 1.87e+01 1.26e+02  -1.8 2.68e+00  -0.1 1.00e+00 6.23e-01f  1
 251r 1.0000059e+04 1.84e+01 2.90e+02  -1.4 1.81e+01  -0.6 7.89e-01 3.19e-01f  1
 252r 1.0000059e+04 1.84e+01 1.93e+02  -1.9 4.99e+00  -0.2 9.38e-01 1.42e-02f  1
 253r 1.0000063e+04 1.82e+01 2.05e+02  -3.0 2.87e+01  -0.6 5.70e-02 1.19e-01f  1
 254r 9.9999903e+03 1.72e+01 5.05e+02  -1.0 1.19e+01  -0.2 1.00e+00 1.00e+00f  1
 255r 9.9999903e+03 1.72e+01 9.99e+02   1.2 0.00e+00    -  0.00e+00 2.96e-07R  6
 256r 9.9999914e+03 1.72e+01 9.98e+02  -4.8 2.74e+02    -  1.63e-01 8.83e-04f  1
 257r 9.9987310e+03 1.63e+01 9.69e+02   1.2 3.91e+03    -  1.23e-01 2.86e-02f  1
 258r 9.9865794e+03 2.02e+01 2.30e+03   1.5 1.08e+02    -  6.92e-02 1.89e-01f  1
 259r 9.9869040e+03 2.73e+01 2.08e+03   1.2 1.76e+04    -  4.99e-04 5.65e-04f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 260r 9.9885289e+03 4.26e+01 1.01e+03   1.2 5.11e+02    -  8.16e-02 5.24e-02f  1
 261r 9.9895698e+03 4.12e+01 9.93e+02  -0.1 1.53e+02    -  1.00e-01 3.33e-02f  1
 262r 9.9748695e+03 5.47e+01 9.52e+02   1.7 2.25e+02    -  2.83e-01 2.87e-01f  1
 263r 9.9829822e+03 3.75e+01 6.14e+02   1.3 7.09e+01    -  6.03e-01 3.77e-01f  1
 264r 9.9955835e+03 1.52e+01 2.39e+02   0.7 3.47e+01    -  8.19e-01 7.51e-01f  1
 265  9.9912727e+03 1.53e+01 9.87e+01   1.2 3.38e+03    -  1.88e-01 2.84e-02f  1
 266  9.1302652e+03 2.96e+01 8.80e+01   1.0 2.13e+03    -  8.30e-02 1.03e-01f  1
 267  8.8643500e+03 5.73e+01 1.11e+02   1.7 1.73e+03    -  2.21e-01 1.23e-01f  1
 268  8.3546851e+03 5.66e+01 1.01e+02   0.6 4.92e+02    -  1.92e-01 1.52e-01f  1
 269  8.0558417e+03 5.75e+01 1.18e+02   0.7 5.71e+02    -  1.31e-01 1.09e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 270  7.6421782e+03 5.58e+01 1.68e+02   1.1 8.98e+02    -  1.60e-01 9.11e-02f  1
 271  6.8804148e+03 6.42e+01 1.24e+02   1.9 2.75e+03    -  5.16e-02 4.31e-02f  1
 272  6.1547577e+03 8.66e+01 3.46e+02   1.6 1.12e+03    -  9.33e-02 1.16e-01f  1
 273  5.9386679e+03 8.31e+01 3.19e+02  -4.7 5.38e+02    -  1.09e-01 7.07e-02f  1
 274  5.6008652e+03 8.01e+01 2.82e+02  -4.8 1.39e+03    -  5.58e-02 6.41e-02f  1
 275  5.2229337e+03 7.09e+01 2.65e+02  -4.8 1.53e+03    -  2.14e-02 8.64e-02f  1
 276  5.0643522e+03 6.30e+01 2.51e+02  -0.9 3.63e+02    -  2.16e-01 1.06e-01f  1
 277  4.6091102e+03 4.92e+01 2.18e+02  -4.9 1.51e+03    -  7.16e-02 1.61e-01f  1
 278  4.4870485e+03 4.58e+01 1.98e+02  -0.6 4.12e+02    -  1.51e-01 9.15e-02f  1
 279  4.0632566e+03 4.85e+01 1.56e+02  -0.9 1.44e+03    -  7.89e-02 1.97e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 280  3.9884866e+03 4.45e+01 1.41e+02  -1.0 3.84e+02    -  1.25e-01 9.27e-02f  1
 281  3.5976736e+03 4.56e+01 1.11e+02  -0.1 1.42e+03    -  7.49e-02 2.05e-01f  1
 282  3.5441851e+03 4.25e+01 1.03e+02  -5.2 4.68e+02    -  1.23e-01 7.40e-02f  1
 283  3.2679053e+03 3.98e+01 8.47e+01  -0.1 1.34e+03    -  5.28e-02 1.76e-01f  1
 284  3.2315085e+03 3.85e+01 8.18e+01  -5.2 8.17e+02    -  1.19e-01 3.43e-02f  1
 285  3.1512123e+03 3.53e+01 7.46e+01  -0.5 8.74e+02    -  3.07e-02 8.74e-02f  1
 286  2.9702302e+03 3.13e+01 1.39e+02  -0.8 1.14e+03    -  2.33e-02 1.47e-01f  1
 287  2.9303268e+03 3.01e+01 1.38e+02  -5.3 8.46e+02    -  7.32e-02 4.27e-02f  1
 288  2.8692000e+03 2.82e+01 1.17e+02  -0.4 9.19e+02    -  7.10e-02 6.32e-02f  1
 289  2.6948892e+03 2.77e+01 1.19e+02  -0.2 1.38e+03    -  4.57e-02 1.26e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 290  2.6385966e+03 2.60e+01 9.13e+01   0.2 6.46e+02    -  6.03e-02 6.34e-02f  1
 291  2.4965528e+03 2.28e+01 6.68e+01  -0.7 9.15e+02    -  3.95e-02 1.52e-01f  1
 292  2.4522013e+03 2.17e+01 6.24e+01  -5.4 5.06e+02    -  6.47e-02 5.66e-02f  1
 293  2.3438699e+03 1.97e+01 5.37e+01  -0.4 7.26e+02    -  9.81e-02 1.04e-01f  1
 294  2.1911773e+03 1.72e+01 4.31e+01  -0.3 8.56e+02    -  9.06e-02 1.30e-01f  1
 295  2.0653520e+03 1.54e+01 6.36e+01  -0.3 9.67e+02    -  2.98e-02 1.23e-01f  1
 296  2.0011075e+03 1.41e+01 5.68e+01  -5.5 5.07e+02    -  5.60e-02 8.56e-02f  1
 297  1.9068268e+03 1.42e+01 4.97e+01  -0.2 1.20e+03    -  5.80e-02 7.45e-02f  1
 298  1.7769023e+03 1.45e+01 5.11e+01  -0.5 5.39e+02    -  7.15e-02 1.73e-01f  1
 299  1.6614643e+03 1.39e+01 1.11e+02  -0.7 5.22e+02    -  3.87e-02 2.23e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 300  1.6283053e+03 1.28e+01 9.35e+01  -1.7 4.46e+02    -  1.05e-01 9.39e-02f  1
 301  1.5832852e+03 1.20e+01 7.98e+01  -1.2 3.02e+02    -  6.94e-02 1.06e-01f  1
 302  1.5360146e+03 1.12e+01 6.77e+01  -1.4 3.00e+02    -  5.14e-02 1.09e-01f  1
 303  1.4327342e+03 1.11e+01 1.29e+02  -1.4 2.59e+02    -  1.31e-02 2.84e-01f  1
 304  1.3851838e+03 8.85e+00 7.82e+01  -1.1 1.45e+02    -  3.14e-02 2.72e-01f  1
 305  1.3673556e+03 8.04e+00 6.87e+01  -1.6 1.45e+02    -  1.06e-01 1.03e-01f  1
 306  1.3479544e+03 7.35e+00 6.02e+01  -1.4 1.62e+02    -  5.49e-02 1.01e-01f  1
 307  1.3280837e+03 6.76e+00 5.31e+01  -1.7 1.75e+02    -  5.47e-02 9.55e-02f  1
 308  1.3075022e+03 6.25e+00 4.70e+01  -1.7 1.90e+02    -  5.53e-02 9.19e-02f  1
 309  1.2863745e+03 5.81e+00 4.17e+01  -1.7 2.01e+02    -  5.38e-02 8.98e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 310  1.2631030e+03 5.41e+00 3.65e+01  -0.8 2.17e+02    -  5.54e-02 9.56e-02f  1
 311  1.2426882e+03 5.04e+00 3.24e+01  -1.5 2.06e+02    -  6.72e-02 8.80e-02f  1
 312  1.2218154e+03 4.71e+00 2.88e+01  -1.2 2.16e+02    -  5.02e-02 8.78e-02f  1
 313  1.1953932e+03 4.27e+00 2.37e+01  -1.1 1.88e+02    -  6.11e-02 1.31e-01f  1
 314  1.1441070e+03 3.45e+00 5.98e+01  -1.4 1.42e+02    -  2.49e-02 3.46e-01f  1
 315  1.1431444e+03 3.40e+00 5.89e+01  -6.0 7.16e+01    -  4.22e-02 1.43e-02h  1
 316  1.1296968e+03 3.10e+00 5.00e+01  -1.5 1.25e+02    -  1.41e-01 1.10e-01f  1
 317  1.1053258e+03 2.26e+00 2.19e+01  -1.7 7.95e+01    -  1.23e-01 3.37e-01f  1
 318  1.1043896e+03 2.20e+00 2.13e+01  -6.1 4.07e+01    -  7.52e-02 2.92e-02h  1
 319  1.0903670e+03 1.51e+00 1.42e+01  -2.0 4.56e+01    -  1.55e-01 3.62e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 320  1.0898578e+03 1.46e+00 1.12e+01  -6.2 3.61e+01    -  1.96e-01 3.86e-02h  1
 321  1.0836726e+03 9.49e-01 5.88e+00  -1.7 5.23e+01    -  4.70e-01 4.21e-01f  1
 322  1.0962919e+03 2.11e+00 5.34e+01  -0.1 5.92e+02    -  3.08e-03 1.63e-01f  1
 323  1.1033871e+03 1.72e+00 3.42e+01  -0.6 1.72e+02    -  9.54e-01 7.15e-01f  1
 324  1.1409484e+03 3.46e-01 6.56e+00  -0.6 1.64e+03    -  1.87e-01 1.00e+00f  1
 325  1.1240217e+03 3.89e-01 2.33e+00  -1.4 2.48e+02    -  9.51e-01 6.44e-01f  1
 326  1.0927889e+03 2.60e-01 5.96e-01  -2.0 1.02e+03    -  1.00e+00 8.57e-01f  1
 327  1.0765398e+03 6.44e-02 1.11e-01  -2.8 1.54e+03    -  9.75e-01 1.00e+00f  1
 328  1.0753091e+03 1.12e-02 2.23e-03  -3.4 2.81e+02    -  9.81e-01 1.00e+00h  1
 329  1.0749881e+03 2.49e-03 2.34e-03  -4.3 6.91e+01    -  8.37e-01 9.94e-01h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 330  1.0749500e+03 3.44e-04 4.02e-05  -4.9 8.24e+00    -  1.00e+00 9.88e-01h  1
 331  1.0749406e+03 5.62e-05 4.38e-05  -5.6 2.06e+00    -  1.00e+00 9.64e-01h  1
 332  1.0749386e+03 7.89e-06 2.67e-05  -6.3 4.66e-01    -  1.00e+00 8.81e-01h  1
 333  1.0749379e+03 1.38e-07 6.78e-08  -7.4 1.55e-01    -  1.00e+00 9.96e-01h  1

Number of Iterations....: 333

                                   (scaled)                 (unscaled)
Objective...............:   1.0749379337400549e+03    1.0749379337400549e+03
Dual infeasibility......:   6.7849130478080360e-08    6.7849130478080360e-08
Constraint violation....:   1.3769067663815804e-07    1.3769067663815804e-07
Complementarity.........:   1.0432651626184988e-07    1.0432651626184988e-07
Overall NLP error.......:   1.3769067663815804e-07    1.3769067663815804e-07


Number of objective function evaluations             = 544
Number of objective gradient evaluations             = 107
Number of equality constraint evaluations            = 544
Number of inequality constraint evaluations          = 544
Number of equality constraint Jacobian evaluations   = 343
Number of inequality constraint Jacobian evaluations = 343
Number of Lagrangian Hessian evaluations             = 333
Total CPU secs in IPOPT (w/o function evaluations)   =      2.340
Total CPU secs in NLP function evaluations           =      3.922

EXIT: Optimal Solution Found.
 
 The solution was found.
 
 The final value of the objective function is    1074.93793374005     
 
 ---------------------------------------------------
 Solver         :  IPOPT (v3.12)
 Solution time  :    6.41460000000370      sec
 Objective      :    1074.93793374005     
 Successful solution
 ---------------------------------------------------
 
Final Time: 10.749373028


#Plot solution
tm = np.linspace(0,tf.value[0],nt)
plt.figure(1)
plt.plot(tm,x.value,'k-',label=r'$x$')
plt.plot(tm,y.value,'b-',label=r'$y$')
plt.plot(tm,v.value,'g-',label=r'$v$')
plt.plot(tm,th.value,'m-',label=r'$\theta$')
plt.plot(tm,uv.value,'r--',label=r'$a_v$')
plt.plot(tm,phi.value,'y--',label=r'$\phi$')
plt.legend(loc='best')
plt.xlabel('Time')
plt.show()

circle3 = plt.Circle((obs_1[0], obs_1[1]), 6.5, color='gray', clip_on=False)
circle2 = plt.Circle((obs_2[0], obs_2[1]), 6.5, color='gray', clip_on=False)
circle1 = plt.Circle((obs_3[0], obs_3[1]), 6.5, color='gray', clip_on=False)

plt.figure(1)
plt.plot(x.value,y.value,'k-',label=r'vehicle')
plt.gcf().gca().add_artist(circle3)
plt.gcf().gca().add_artist(circle2)
plt.gcf().gca().add_artist(circle1)
plt.legend(loc='upper left')
plt.xlabel('x position')
plt.ylabel('y position')
plt.ylim([0,50])
plt.xlim([0,50])
plt.show()


altitude = 150

# initialize GEKKO
m = GEKKO() 
nt = 101
m.time = np.linspace(0,1,nt)

# Variables
s = m.Var(value=0)
v = m.Var(value=0, lb=0, ub=8)
m_v = m.Var(value=2) 

# optimize final time
tf = m.FV(value=1.0,lb=0.1,ub=100.0)
tf.STATUS = 1

# control changes every time period
u = m.MV(value=0, lb=-2,ub=2)
u.STATUS = 1

# define the ODEs that describe the movement of the vehicle
m.Equation(s.dt()==v*tf)
m.Equation(v.dt()*m_v==(u-0.2*v**2)*tf)
m.Equation(m_v.dt()==tf*(-0.01*u**2))

# define path constraints
m.Equation(s >= 0)


# define boundary constraints
m.fix(s, pos=len(m.time)-1,val=altitude)
m.fix(v, pos=len(m.time)-1,val=0)

# Objective function
m.Obj(tf)

# Solve
m.options.IMODE = 6
m.options.MAX_ITER = 1000
m.solve(disp=True) # set to True to view solver logs

#Presentation of results
print('Final Time: ' + str(tf.value[0]))

apm 155.198.90.49_gk_model6 <br><pre> ----------------------------------------------------------------
 APMonitor, Version 1.0.0
 APMonitor Optimization Suite
 ----------------------------------------------------------------
 
 
 --------- APM Model Size ------------
 Each time step contains
   Objects      :            0
   Constants    :            0
   Variables    :            6
   Intermediates:            0
   Connections  :            4
   Equations    :            5
   Residuals    :            5
 
 Number of state variables:           1197
 Number of total equations: -         1100
 Number of slack variables: -          100
 ---------------------------------------
 Degrees of freedom       :             -3
 
 * Warning: DOF <= 0
 **********************************************
 Dynamic Control with Interior Point Solver
 **********************************************
  
  
 Info: Exact Hessian

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

This is Ipopt version 3.12.10, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...:     2687
Number of nonzeros in inequality constraint Jacobian.:      400
Number of nonzeros in Lagrangian Hessian.............:      497

Total number of variables............................:     1197
                     variables with only lower bounds:      300
                variables with lower and upper bounds:      200
                     variables with only upper bounds:        0
Total number of equality constraints.................:      900
Total number of inequality constraints...............:      200
        inequality constraints with only lower bounds:      200
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.0000012e+02 1.50e+02 1.00e+02   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  2.1159917e+03 1.50e+02 7.45e+02   1.8 1.47e+04    -  1.12e-04 2.51e-03f  1
   2  2.1468385e+03 1.49e+02 7.44e+02   0.1 4.37e+03    -  6.11e-04 9.67e-04h  1
   3  2.1552266e+03 1.49e+02 7.44e+02   0.1 1.04e+04    -  8.94e-04 3.22e-04h  1
   4  2.4155190e+03 1.48e+02 7.26e+02   0.1 2.02e+03  -2.0 7.07e-04 1.03e-02h  1
   5  2.4248712e+03 1.48e+02 7.26e+02   0.1 2.71e+04  -2.5 2.13e-04 2.72e-04h  1
   6  2.4883285e+03 1.47e+02 7.24e+02   0.1 2.63e+03  -2.1 1.12e-02 2.72e-03h  1
   7  2.5111061e+03 1.47e+02 7.23e+02   0.1 9.69e+03  -2.5 1.73e-03 8.79e-04h  1
   8  2.6511502e+03 1.46e+02 7.16e+02   0.1 2.32e+03  -2.1 8.66e-03 6.04e-03h  1
   9  2.7243030e+03 1.46e+02 7.14e+02   0.1 6.54e+03  -2.6 7.68e-04 3.05e-03h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  2.8403651e+03 1.45e+02 7.09e+02   0.1 1.94e+03  -2.2 1.98e-02 5.35e-03h  1
  11  2.8901469e+03 1.45e+02 7.07e+02   0.1 4.13e+03  -2.6 4.10e-03 2.33e-03h  1
  12  3.1308832e+03 1.43e+02 6.93e+02   0.1 1.40e+03  -2.2 6.33e-03 1.21e-02h  1
  13  3.1554287e+03 1.43e+02 6.92e+02   0.1 6.68e+03  -2.7 2.68e-03 1.14e-03h  1
  14  3.4013447e+03 1.41e+02 6.77e+02   0.1 1.31e+03  -2.3 1.28e-02 1.43e-02h  1
  15  3.4776492e+03 1.40e+02 6.74e+02   0.1 6.12e+03  -2.7 2.82e-04 3.72e-03h  1
  16  3.4868802e+03 1.40e+02 6.74e+02   0.1 7.19e+04  -3.2 1.60e-03 2.30e-04h  1
  17  3.7152207e+03 1.38e+02 6.60e+02   0.1 3.16e+03  -2.8 1.55e-02 1.46e-02h  1
  18  3.8416946e+03 1.37e+02 6.54e+02   0.1 1.02e+04  -3.3 9.12e-03 6.96e-03h  1
  19  3.8537697e+03 1.37e+02 6.53e+02   0.1 7.85e+03  -2.8 1.17e-02 1.10e-03h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20  3.9775252e+03 1.36e+02 6.47e+02   0.1 1.58e+04  -3.3 5.02e-03 7.68e-03h  1
  21  3.9821491e+03 1.36e+02 6.47e+02   0.1 6.50e+03  -2.9 9.92e-04 4.12e-04h  1
  22  4.0480158e+03 1.35e+02 6.43e+02   0.1 5.47e+03  -2.5 5.81e-03 6.09e-03h  1
  23  4.1641035e+03 1.34e+02 6.36e+02   0.1 7.91e+03  -2.9 1.16e-03 9.28e-03h  1
  24  4.2031095e+03 1.33e+02 6.33e+02   0.1 5.69e+03  -2.5 1.68e-03 4.90e-03h  1
  25  4.2454566e+03 1.33e+02 6.29e+02   0.1 7.22e+03  -3.0 8.56e-03 5.68e-03h  1
  26  4.2550963e+03 1.32e+02 6.28e+02   0.1 4.45e+03  -2.6 3.14e-03 2.47e-03h  1
  27  4.2611543e+03 1.32e+02 6.27e+02   0.1 1.06e+04  -3.0 5.80e-03 7.17e-04h  1
  28  4.3282063e+03 1.31e+02 6.23e+02   0.1 5.69e+03  -2.6 2.24e-04 6.40e-03h  1
  29  4.4145509e+03 1.30e+02 6.18e+02   0.1 8.31e+03  -3.1 1.18e-02 7.04e-03h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  30  4.5398522e+03 1.29e+02 6.10e+02   0.1 6.17e+03  -2.7 5.15e-03 1.17e-02h  1
  31  4.6106152e+03 1.28e+02 6.07e+02   0.1 9.19e+03  -3.1 2.53e-02 5.37e-03h  1
  32  4.6597966e+03 1.27e+02 6.02e+02   0.1 8.29e+03  -2.7 2.65e-03 6.62e-03h  1
  33  4.7593991e+03 1.26e+02 5.96e+02   0.1 1.15e+04  -3.2 3.65e-03 1.04e-02h  1
  34  4.7608485e+03 1.26e+02 5.96e+02   0.1 1.01e+04  -2.8 1.76e-03 2.42e-04h  1
  35  4.7825513e+03 1.25e+02 5.92e+02   0.1 6.73e+03  -3.2 1.73e-04 5.16e-03h  1
  36  4.7806238e+03 1.25e+02 5.91e+02   0.1 1.06e+04  -2.8 2.82e-03 2.32e-03f  1
  37  4.8690632e+03 1.24e+02 5.85e+02   0.1 6.49e+03  -3.3 7.57e-04 1.05e-02h  1
  38  4.9096187e+03 1.23e+02 5.82e+02   0.1 8.29e+03  -2.9 5.66e-03 3.81e-03h  1
  39  4.9905685e+03 1.22e+02 5.77e+02   0.1 7.63e+03  -3.3 2.21e-03 8.85e-03h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  40  4.9977272e+03 1.22e+02 5.76e+02   0.1 9.70e+03  -2.9 2.92e-03 6.69e-04h  1
  41  5.1254581e+03 1.21e+02 5.68e+02   0.1 9.17e+03  -3.4 1.30e-03 1.27e-02h  1
  42  5.1714418e+03 1.20e+02 5.65e+02   0.1 9.47e+03  -3.0 1.51e-02 5.14e-03h  1
  43  5.2137645e+03 1.19e+02 5.63e+02   0.1 1.32e+04  -3.4 2.41e-02 4.26e-03h  1
  44  5.2246878e+03 1.18e+02 5.57e+02   0.1 1.10e+04  -3.0 6.48e-04 9.78e-03f  1
  45  5.2708820e+03 1.17e+02 5.49e+02   0.1 9.27e+03  -3.5 2.56e-03 1.39e-02h  1
  46  5.3449961e+03 1.15e+02 5.44e+02   0.1 7.12e+03    -  1.62e-02 1.01e-02h  1
  47  5.4445532e+03 1.14e+02 5.39e+02   0.1 7.31e+03    -  1.00e-02 8.30e-03h  1
  48  5.8123573e+03 1.11e+02 5.16e+02   0.1 7.26e+03    -  1.36e-02 3.39e-02h  1
  49  5.8148587e+03 1.10e+02 5.16e+02   0.1 3.24e+03  -3.1 6.13e-03 7.54e-04h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  50  5.8539088e+03 1.09e+02 5.09e+02   0.1 8.50e+03  -3.6 4.54e-03 1.31e-02f  1
  51  5.8769360e+03 1.08e+02 5.04e+02   0.1 1.32e+04    -  1.27e-03 1.03e-02h  1
  52  5.8591761e+03 1.07e+02 5.01e+02   0.1 1.62e+04    -  4.42e-03 5.09e-03f  1
  53  5.9022160e+03 1.05e+02 4.92e+02   0.1 6.14e+03    -  2.20e-03 1.88e-02f  1
  54  6.3108821e+03 9.92e+01 4.58e+02   0.1 3.31e+03    -  1.26e-02 5.81e-02h  1
  55  6.5689765e+03 9.49e+01 4.36e+02   0.1 3.47e+03    -  5.92e-02 4.36e-02h  1
  56  6.6318125e+03 9.36e+01 4.30e+02   0.1 2.30e+03    -  1.07e-02 1.33e-02h  1
  57  7.3442335e+03 8.09e+01 3.58e+02   0.1 1.90e+03    -  4.25e-02 1.36e-01h  1
  58  7.6031900e+03 7.50e+01 3.31e+02   0.1 1.77e+03    -  7.89e-02 7.19e-02h  1
  59  7.6574333e+03 7.35e+01 3.24e+02   0.1 6.80e+02    -  1.12e-02 2.07e-02h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  60  8.3404563e+03 5.64e+01 2.38e+02   0.1 9.26e+02    -  9.00e-02 2.32e-01h  1
  61  8.6060825e+03 4.53e+01 1.89e+02   0.1 6.27e+02    -  1.13e-01 1.97e-01h  1
  62  8.6951301e+03 3.60e+01 1.49e+02   0.1 3.87e+02    -  1.21e-01 2.07e-01f  1
  63  8.5983148e+03 2.75e+01 1.15e+02   0.1 4.34e+02    -  1.20e-01 2.34e-01f  1
  64  8.3878756e+03 2.27e+01 9.28e+01   0.1 4.91e+02    -  1.17e-01 1.97e-01f  1
  65  8.0498830e+03 2.72e+01 1.60e+02   0.1 5.27e+02    -  1.13e-01 2.27e-01f  1
  66  7.7124691e+03 2.63e+01 2.16e+02   0.1 7.19e+02    -  1.11e-01 1.95e-01f  1
  67  7.3640482e+03 2.45e+01 2.67e+02   0.1 6.25e+02    -  1.14e-01 1.85e-01f  1
  68  6.9682704e+03 2.64e+01 3.21e+02   0.1 4.12e+02    -  1.31e-01 1.99e-01f  1
  69  6.5133092e+03 3.19e+01 4.25e+02   0.1 4.41e+02    -  1.27e-01 2.16e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  70  5.9769406e+03 3.64e+01 5.69e+02   0.1 3.51e+02    -  1.52e-01 2.56e-01f  1
  71  5.4356934e+03 3.48e+01 7.02e+02   0.1 3.17e+02    -  1.77e-01 2.66e-01f  1
  72  4.9489790e+03 3.43e+01 8.27e+02   0.1 3.58e+02    -  1.90e-01 2.66e-01f  1
  73  4.8248875e+03 3.27e+01 4.74e+01   0.1 9.96e+02    -  2.77e-01 1.26e-01f  1
  74  4.8289975e+03 3.22e+01 8.60e+02   0.1 6.60e+02    -  1.75e-01 1.63e-02h  1
  75  4.9660336e+03 2.13e+01 1.43e+03   0.1 4.54e+02    -  7.63e-01 5.44e-01f  1
  76  5.0321887e+03 2.14e+01 6.28e+02   0.1 3.48e+02    -  3.86e-01 4.25e-01f  1
  77  5.2780566e+03 9.59e-01 4.96e+03   0.1 1.41e+02    -  9.06e-02 1.00e+00f  1
  78  5.1574203e+03 1.79e+00 1.56e+03  -0.1 1.13e+02    -  8.05e-01 1.00e+00f  1
  79  5.1549198e+03 2.72e+00 1.15e+03   0.1 1.17e+03    -  3.81e-01 4.71e-02f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  80  5.1046833e+03 2.05e+00 4.32e+02  -0.4 4.10e+02    -  7.38e-01 6.61e-01f  1
  81  5.0712395e+03 5.49e-01 5.98e+01  -1.8 5.37e+01    -  9.91e-01 6.29e-01f  1
  82  5.0461563e+03 2.30e-02 2.05e-01  -2.9 5.28e+02    -  1.00e+00 9.92e-01f  1
  83  5.0450449e+03 1.95e-04 2.57e-02  -4.3 3.88e+02    -  9.99e-01 9.92e-01f  1
  84  5.0450168e+03 9.12e-07 5.04e-02  -4.8 1.17e+01    -  1.00e+00 9.95e-01h  1
  85  5.0450104e+03 1.68e-07 2.91e+00  -6.5 2.96e+00    -  1.00e+00 8.16e-01f  1
  86  5.0450090e+03 9.98e-09 5.70e-03  -6.5 5.36e-01    -  1.00e+00 1.00e+00h  1
  87  5.0450089e+03 1.00e-08 4.81e-01  -8.4 5.80e-02    -  1.00e+00 9.89e-01f  1
  88  5.0450089e+03 1.00e-08 6.02e-13  -9.9 1.41e-03    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 88

                                   (scaled)                 (unscaled)
Objective...............:   5.0450088533388971e+03    5.0450088533388971e+03
Dual infeasibility......:   6.0232104778882708e-13    6.0232104778882708e-13
Constraint violation....:   9.9999907361236115e-09    9.9999907361236115e-09
Complementarity.........:   1.9072438640913431e-10    1.9072438640913431e-10
Overall NLP error.......:   9.9999907361236115e-09    9.9999907361236115e-09


Number of objective function evaluations             = 89
Number of objective gradient evaluations             = 89
Number of equality constraint evaluations            = 89
Number of inequality constraint evaluations          = 89
Number of equality constraint Jacobian evaluations   = 89
Number of inequality constraint Jacobian evaluations = 89
Number of Lagrangian Hessian evaluations             = 88
Total CPU secs in IPOPT (w/o function evaluations)   =      0.283
Total CPU secs in NLP function evaluations           =      0.593

EXIT: Optimal Solution Found.
 
 The solution was found.
 
 The final value of the objective function is    5045.00885333890     
 
 ---------------------------------------------------
 Solver         :  IPOPT (v3.12)
 Solution time  :   0.898000000001048      sec
 Objective      :    5045.00885333890     
 Successful solution
 ---------------------------------------------------
 
Final Time: 50.45008587


tm = np.linspace(0,tf.value[0],nt)
plt.figure(1)
plt.subplot(4, 1, 1)
plt.plot(tm, s.value, 'k-',label=r'$s$')
plt.legend(loc='best')
plt.ylabel('Position')
plt.xlabel('Time')

plt.subplot(4, 1, 2)
plt.plot(tm, v.value, 'b-',label=r'$v$')
plt.legend(loc='upper left')
plt.ylabel('Velocity')
plt.xlabel('Time')

plt.subplot(4, 1, 3)
plt.plot(tm, m_v.value, 'm-',label=r'$m$')
plt.legend(loc='upper left')
plt.ylabel('Mass')
plt.xlabel('Time')

plt.subplot(4, 1, 4)
plt.plot(tm, u.value, 'r-',label=r'$u$')
plt.legend(loc='upper left')
plt.ylabel('Force')
plt.xlabel('Time')
plt.show()

Notebook 7.3 - Tutorial Solutions using Python and Gekko¶

Question 1¶

Question 2¶