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opt11_output.txt
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opt11_output.txt
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>> opt11_run
---------------------------------------------------------
Running testcase_11: (unconstrained) solution (0, 0, 0)
---------------------------------------------------------
Newton:
-------------------------------------------------------
minimization of "opt11_fgh" performed using newton.
globalization is handled using trust_region.
stopping criteria are:
gradient < 1.000000e-06, step < 1.000000e-06,
in addition, no more than 2000 iterations
or 2000 function evaluations are permitted.
-------------------------------------------------------
Initial Point:
-------------------------------------------------------
Design Variables: 1.00000000e+01, 1.00000000e+01, 1.00000000e+01
Initial Function: 4.01000000e+04
Norm of Gradient: 1.26491265e+04
Iteration 1
-------------------------------------------------------
Design Variables: 9.99971763e+00, 9.99990587e+00, 9.99999953e+00
Function Value: 4.00962352e+04
Step: -2.82371038e-04, -9.41289951e-05, -4.70658245e-07
Gradient: 1.19989835e+04, 3.99988705e+03, 1.99999991e+01
Norm of Step: 2.97647261e-04
Norm of Gradient: 1.26481264e+04
Iteration 2
-------------------------------------------------------
Design Variables: 9.99915274e+00, 9.99971754e+00, 9.99999859e+00
Function Value: 4.00887044e+04
Step: -5.64888294e-04, -1.88328009e-04, -9.41719710e-07
Gradient: 1.19969501e+04, 3.99966106e+03, 1.99999972e+01
Norm of Step: 5.95455381e-04
Norm of Gradient: 1.26461259e+04
Iteration 3
-------------------------------------------------------
Design Variables: 9.99802340e+00, 9.99934095e+00, 9.99999670e+00
Function Value: 4.00736518e+04
Step: -1.12934162e-03, -3.76596065e-04, -1.88335206e-06
Gradient: 1.19928856e+04, 3.99920919e+03, 1.99999934e+01
Norm of Step: 1.19047916e-03
Norm of Gradient: 1.26421272e+04
Iteration 4
-------------------------------------------------------
Design Variables: 9.99576482e+00, 9.99858745e+00, 9.99999294e+00
Function Value: 4.00435609e+04
Step: -2.25858108e-03, -7.53498426e-04, -3.76908651e-06
Gradient: 1.19847598e+04, 3.99830518e+03, 1.99999859e+01
Norm of Step: 2.38095833e-03
Norm of Gradient: 1.26341328e+04
Iteration 5
-------------------------------------------------------
Design Variables: 9.99124807e+00, 9.99707923e+00, 9.99998539e+00
Function Value: 3.99834363e+04
Step: -4.51675297e-03, -1.50822278e-03, -7.54771502e-06
Gradient: 1.19685206e+04, 3.99649609e+03, 1.99999708e+01
Norm of Step: 4.76191666e-03
Norm of Gradient: 1.26181562e+04
Iteration 6
-------------------------------------------------------
Design Variables: 9.98221620e+00, 9.99405787e+00, 9.99997025e+00
Function Value: 3.98634151e+04
Step: -9.03186496e-03, -3.02135526e-03, -1.51336974e-05
Gradient: 1.19360921e+04, 3.99287368e+03, 1.99999405e+01
Norm of Step: 9.52383333e-03
Norm of Gradient: 1.25862518e+04
Iteration 7
-------------------------------------------------------
Design Variables: 9.96415907e+00, 9.98799547e+00, 9.99993983e+00
Function Value: 3.96242826e+04
Step: -1.80571326e-02, -6.06239725e-03, -3.04212638e-05
Gradient: 1.18714345e+04, 3.98561185e+03, 1.99998797e+01
Norm of Step: 1.90476672e-02
Norm of Gradient: 1.25226379e+04
Iteration 8
-------------------------------------------------------
Design Variables: 9.92807145e+00, 9.97579155e+00, 9.99987837e+00
Function Value: 3.91496404e+04
Step: -3.60876130e-02, -1.22039276e-02, -6.14644780e-05
Gradient: 1.17429153e+04, 3.97102012e+03, 1.99997567e+01
Norm of Step: 3.80953467e-02
Norm of Gradient: 1.23961873e+04
Iteration 9
-------------------------------------------------------
Design Variables: 9.85600492e+00, 9.95106405e+00, 9.99975290e+00
Function Value: 3.82147076e+04
Step: -7.20665389e-02, -2.47274986e-02, -1.25469727e-04
Gradient: 1.14890463e+04, 3.94156376e+03, 1.99995058e+01
Norm of Step: 7.61908850e-02
Norm of Gradient: 1.21463785e+04
Iteration 10
-------------------------------------------------------
Design Variables: 9.71232590e+00, 9.90030635e+00, 9.99949136e+00
Function Value: 3.64011750e+04
Step: -1.43679012e-01, -5.07576973e-02, -2.61540103e-04
Gradient: 1.09938799e+04, 3.88155632e+03, 1.99989827e+01
Norm of Step: 1.52381333e-01
Norm of Gradient: 1.16589997e+04
Iteration 11
-------------------------------------------------------
Design Variables: 9.42693566e+00, 9.79338411e+00, 9.99892205e+00
Function Value: 3.29908708e+04
Step: -2.85390246e-01, -1.06922244e-01, -5.69310700e-04
Gradient: 1.00529350e+04, 3.75714846e+03, 1.99978441e+01
Norm of Step: 3.04762666e-01
Norm of Gradient: 1.07321045e+04
Iteration 12
-------------------------------------------------------
Design Variables: 8.86537222e+00, 9.55639086e+00, 9.99756206e+00
Function Value: 2.69715744e+04
Step: -5.61563434e-01, -2.36993242e-01, -1.35998358e-03
Gradient: 8.36126851e+03, 3.49093454e+03, 1.99951241e+01
Norm of Step: 6.09525337e-01
Norm of Gradient: 9.06078555e+03
Iteration 13
-------------------------------------------------------
Design Variables: 7.79143048e+00, 8.97957426e+00, 9.99352930e+00
Function Value: 1.76573086e+04
Step: -1.07394174e+00, -5.76816605e-01, -4.03275898e-03
Gradient: 5.67587531e+03, 2.89619121e+03, 1.99870586e+01
Norm of Step: 1.21905066e+00
Norm of Gradient: 6.37211766e+03
Iteration 14
-------------------------------------------------------
Design Variables: 5.93269560e+00, 7.40194410e+00, 9.97056077e+00
Function Value: 6.81768257e+03
Step: -1.85873488e+00, -1.57763016e+00, -2.29685392e-02
Gradient: 2.50574829e+03, 1.62217384e+03, 1.99411215e+01
Norm of Step: 2.43810169e+00
Norm of Gradient: 2.98506618e+03
Iteration 15
-------------------------------------------------------
Design Variables: 3.96035448e+00, 4.94716008e+00, 6.24748965e+00
Function Value: 1.37602896e+03
Step: -1.97234112e+00, -2.45478402e+00, -3.72307111e+00
Gradient: 7.45389766e+02, 4.84314957e+02, 1.24949793e+01
Norm of Step: 4.87620268e+00
Norm of Gradient: 8.89001127e+02
Iteration 16
-------------------------------------------------------
Design Variables: 2.64023632e+00, 3.29810672e+00, 8.88178420e-16
Function Value: 2.64098336e+02
Step: -1.32011816e+00, -1.64905336e+00, -6.24748965e+00
Gradient: 2.20856227e+02, 1.43500728e+02, 1.77635684e-15
Norm of Step: 6.59493866e+00
Norm of Gradient: 2.63381723e+02
Iteration 17
-------------------------------------------------------
Design Variables: 1.76015755e+00, 2.19873781e+00, 9.86076132e-32
Function Value: 5.21675726e+01
Step: -8.80078773e-01, -1.09936891e+00, -8.88178420e-16
Gradient: 6.54388820e+01, 4.25187342e+01, 1.97215226e-31
Norm of Step: 1.40824381e+00
Norm of Gradient: 7.80390289e+01
Iteration 18
-------------------------------------------------------
Design Variables: 1.17343836e+00, 1.46582521e+00, 1.09476443e-47
Function Value: 1.03047057e+01
Step: -5.86719182e-01, -7.32912604e-01, -9.86076132e-32
Gradient: 1.93892984e+01, 1.25981435e+01, 2.18952885e-47
Norm of Step: 9.38829209e-01
Norm of Gradient: 2.31226752e+01
Iteration 19
-------------------------------------------------------
Design Variables: 7.82292242e-01, 9.77216805e-01, 1.21543267e-63
Function Value: 2.03549742e+00
Step: -3.91146121e-01, -4.88608403e-01, -1.09476443e-47
Gradient: 5.74497730e+00, 3.73278325e+00, 2.43086534e-63
Norm of Step: 6.25886139e-01
Norm of Gradient: 6.85116303e+00
Iteration 20
-------------------------------------------------------
Design Variables: 5.21528162e-01, 6.51477870e-01, 1.34940134e-79
Function Value: 4.02073565e-01
Step: -2.60764081e-01, -3.25738935e-01, -1.21543267e-63
Gradient: 1.70221550e+00, 1.10600985e+00, 2.69880267e-79
Norm of Step: 4.17257426e-01
Norm of Gradient: 2.02997423e+00
Iteration 21
-------------------------------------------------------
Design Variables: 3.47685441e-01, 4.34318580e-01, 1.49813643e-95
Function Value: 7.94219388e-02
Step: -1.73842721e-01, -2.17159290e-01, -1.34940134e-79
Gradient: 5.04360147e-01, 3.27706623e-01, 2.99627287e-95
Norm of Step: 2.78171617e-01
Norm of Gradient: 6.01473847e-01
Iteration 22
-------------------------------------------------------
Design Variables: 2.31790294e-01, 2.89545720e-01, 1.66326556e-111
Function Value: 1.56882842e-02
Step: -1.15895147e-01, -1.44772860e-01, -1.49813643e-95
Gradient: 1.49440044e-01, 9.70982585e-02, 3.32653113e-111
Norm of Step: 1.85447745e-01
Norm of Gradient: 1.78214473e-01
Iteration 23
-------------------------------------------------------
Design Variables: 1.54526863e-01, 1.93030480e-01, 1.84659572e-127
Function Value: 3.09892034e-03
Step: -7.72634314e-02, -9.65152400e-02, -1.66326556e-111
Gradient: 4.42785314e-02, 2.87698544e-02, 3.69319145e-127
Norm of Step: 1.23631830e-01
Norm of Gradient: 5.28042883e-02
Iteration 24
-------------------------------------------------------
Design Variables: 1.03017908e-01, 1.28686987e-01, 2.05013309e-143
Function Value: 6.12132412e-04
Step: -5.15089542e-02, -6.43434934e-02, -1.84659572e-127
Gradient: 1.31195649e-02, 8.52440130e-03, 4.10026618e-143
Norm of Step: 8.24212200e-02
Norm of Gradient: 1.56457151e-02
Iteration 25
-------------------------------------------------------
Design Variables: 6.86786056e-02, 8.57913245e-02, 2.27610496e-159
Function Value: 1.20915044e-04
Step: -3.43393028e-02, -4.28956622e-02, -2.05013309e-143
Gradient: 3.88727848e-03, 2.52574853e-03, 4.55220992e-159
Norm of Step: 5.49474800e-02
Norm of Gradient: 4.63576742e-03
Iteration 26
-------------------------------------------------------
Design Variables: 4.57857371e-02, 5.71942163e-02, 2.52698413e-175
Function Value: 2.38844532e-05
Step: -2.28928685e-02, -2.85971082e-02, -2.27610496e-159
Gradient: 1.15178622e-03, 7.48369936e-04, 5.05396826e-175
Norm of Step: 3.66316533e-02
Norm of Gradient: 1.37356072e-03
Iteration 27
-------------------------------------------------------
Design Variables: 3.05238247e-02, 3.81294775e-02, 2.80551597e-191
Function Value: 4.71791668e-06
Step: -1.52619124e-02, -1.90647388e-02, -2.52698413e-175
Gradient: 3.41269990e-04, 2.21739240e-04, 5.61103193e-191
Norm of Step: 2.44211022e-02
Norm of Gradient: 4.06980954e-04
Iteration 28
-------------------------------------------------------
Design Variables: 2.03492165e-02, 2.54196517e-02, 3.11474842e-207
Function Value: 9.31934160e-07
Step: -1.01746082e-02, -1.27098258e-02, -2.80551597e-191
Gradient: 1.01117034e-04, 6.57005156e-05, 6.22949684e-207
Norm of Step: 1.62807348e-02
Norm of Gradient: 1.20586949e-04
Iteration 29
-------------------------------------------------------
Design Variables: 1.35661443e-02, 1.69464345e-02, 3.45806541e-223
Function Value: 1.84085760e-07
Step: -6.78307216e-03, -8.47321723e-03, -3.11474842e-207
Gradient: 2.99606027e-05, 1.94668194e-05, 6.91613083e-223
Norm of Step: 1.08538232e-02
Norm of Gradient: 3.57294664e-05
Iteration 30
-------------------------------------------------------
Design Variables: 9.04409622e-03, 1.12976230e-02, 3.83922384e-239
Function Value: 3.63626193e-08
Step: -4.52204811e-03, -5.64881149e-03, -3.45806541e-223
Gradient: 8.87721561e-06, 5.76794650e-06, 7.67844769e-239
Norm of Step: 7.23588214e-03
Norm of Gradient: 1.05865086e-05
Iteration 31
-------------------------------------------------------
Design Variables: 6.02939748e-03, 7.53174865e-03, 4.26239471e-255
Function Value: 7.18273961e-09
Step: -3.01469874e-03, -3.76587433e-03, -3.83922384e-239
Gradient: 2.63028611e-06, 1.70902119e-06, 8.52478942e-255
Norm of Step: 4.82392143e-03
Norm of Gradient: 3.13674328e-06
Iteration 32
-------------------------------------------------------
Design Variables: 4.01959832e-03, 5.02116577e-03, 4.73220874e-271
Function Value: 1.41881276e-09
Step: -2.00979916e-03, -2.51058288e-03, -4.26239471e-255
Gradient: 7.79344031e-07, 5.06376648e-07, 9.46441749e-271
Norm of Step: 3.21594762e-03
Norm of Gradient: 9.29405417e-07
Gradient is within tolerance, x likely a local optimum.
Optimization required 33 function/gradient evaluations
Trust-region produced [4.0195983e-03,5.0211658e-03,4.7322087e-271)
Value of F(X) = 1.4188128e-09
Newton (constrained x>=1):
Running testcase_11: (constrained) solution (1, 0, 0)
-------------------------------------------------------
minimization of "opt11_fgh" performed using newton.
globalization is handled using trust_region.
stopping criteria are:
gradient < 1.000000e-06, step < 1.000000e-06,
in addition, no more than 2000 iterations
or 2000 function evaluations are permitted.
-------------------------------------------------------
Initial Point:
-------------------------------------------------------
Design Variables: 1.00000000e+01, 1.00000000e+01, 1.00000000e+01
Initial Function: 4.01000000e+04
Norm of Gradient: 1.26491265e+04
Iteration 1
-------------------------------------------------------
Design Variables: 9.99971763e+00, 9.99990587e+00, 9.99999953e+00
Function Value: 4.00962352e+04
Step: -2.82371038e-04, -9.41289951e-05, -4.70658245e-07
Gradient: 1.19989835e+04, 3.99988705e+03, 1.99999991e+01
Norm of Step: 2.97647261e-04
Norm of Gradient: 1.26481264e+04
Iteration 2
-------------------------------------------------------
Design Variables: 9.99915274e+00, 9.99971754e+00, 9.99999859e+00
Function Value: 4.00887044e+04
Step: -5.64888294e-04, -1.88328009e-04, -9.41719710e-07
Gradient: 1.19969501e+04, 3.99966106e+03, 1.99999972e+01
Norm of Step: 5.95455381e-04
Norm of Gradient: 1.26461259e+04
Iteration 3
-------------------------------------------------------
Design Variables: 9.99802340e+00, 9.99934095e+00, 9.99999670e+00
Function Value: 4.00736518e+04
Step: -1.12934162e-03, -3.76596065e-04, -1.88335206e-06
Gradient: 1.19928856e+04, 3.99920919e+03, 1.99999934e+01
Norm of Step: 1.19047916e-03
Norm of Gradient: 1.26421272e+04
Iteration 4
-------------------------------------------------------
Design Variables: 9.99576482e+00, 9.99858745e+00, 9.99999294e+00
Function Value: 4.00435609e+04
Step: -2.25858108e-03, -7.53498426e-04, -3.76908651e-06
Gradient: 1.19847598e+04, 3.99830518e+03, 1.99999859e+01
Norm of Step: 2.38095833e-03
Norm of Gradient: 1.26341328e+04
Iteration 5
-------------------------------------------------------
Design Variables: 9.99124807e+00, 9.99707923e+00, 9.99998539e+00
Function Value: 3.99834363e+04
Step: -4.51675297e-03, -1.50822278e-03, -7.54771502e-06
Gradient: 1.19685206e+04, 3.99649609e+03, 1.99999708e+01
Norm of Step: 4.76191666e-03
Norm of Gradient: 1.26181562e+04
Iteration 6
-------------------------------------------------------
Design Variables: 9.98221620e+00, 9.99405787e+00, 9.99997025e+00
Function Value: 3.98634151e+04
Step: -9.03186496e-03, -3.02135526e-03, -1.51336974e-05
Gradient: 1.19360921e+04, 3.99287368e+03, 1.99999405e+01
Norm of Step: 9.52383333e-03
Norm of Gradient: 1.25862518e+04
Iteration 7
-------------------------------------------------------
Design Variables: 9.96415907e+00, 9.98799547e+00, 9.99993983e+00
Function Value: 3.96242826e+04
Step: -1.80571326e-02, -6.06239725e-03, -3.04212638e-05
Gradient: 1.18714345e+04, 3.98561185e+03, 1.99998797e+01
Norm of Step: 1.90476672e-02
Norm of Gradient: 1.25226379e+04
Iteration 8
-------------------------------------------------------
Design Variables: 9.92807145e+00, 9.97579155e+00, 9.99987837e+00
Function Value: 3.91496404e+04
Step: -3.60876130e-02, -1.22039276e-02, -6.14644780e-05
Gradient: 1.17429153e+04, 3.97102012e+03, 1.99997567e+01
Norm of Step: 3.80953467e-02
Norm of Gradient: 1.23961873e+04
Iteration 9
-------------------------------------------------------
Design Variables: 9.85600492e+00, 9.95106405e+00, 9.99975290e+00
Function Value: 3.82147076e+04
Step: -7.20665389e-02, -2.47274986e-02, -1.25469727e-04
Gradient: 1.14890463e+04, 3.94156376e+03, 1.99995058e+01
Norm of Step: 7.61908850e-02
Norm of Gradient: 1.21463785e+04
Iteration 10
-------------------------------------------------------
Design Variables: 9.71232590e+00, 9.90030635e+00, 9.99949136e+00
Function Value: 3.64011750e+04
Step: -1.43679012e-01, -5.07576973e-02, -2.61540103e-04
Gradient: 1.09938799e+04, 3.88155632e+03, 1.99989827e+01
Norm of Step: 1.52381333e-01
Norm of Gradient: 1.16589997e+04
Iteration 11
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Design Variables: 9.42693566e+00, 9.79338411e+00, 9.99892205e+00
Function Value: 3.29908708e+04
Step: -2.85390246e-01, -1.06922244e-01, -5.69310700e-04
Gradient: 1.00529350e+04, 3.75714846e+03, 1.99978441e+01
Norm of Step: 3.04762666e-01
Norm of Gradient: 1.07321045e+04
Iteration 12
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Design Variables: 8.86537222e+00, 9.55639086e+00, 9.99756206e+00
Function Value: 2.69715744e+04
Step: -5.61563434e-01, -2.36993242e-01, -1.35998358e-03
Gradient: 8.36126851e+03, 3.49093454e+03, 1.99951241e+01
Norm of Step: 6.09525337e-01
Norm of Gradient: 9.06078555e+03
Iteration 13
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Design Variables: 7.79143048e+00, 8.97957426e+00, 9.99352930e+00
Function Value: 1.76573086e+04
Step: -1.07394174e+00, -5.76816605e-01, -4.03275898e-03
Gradient: 5.67587531e+03, 2.89619121e+03, 1.99870586e+01
Norm of Step: 1.21905066e+00
Norm of Gradient: 6.37211766e+03
Iteration 14
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Design Variables: 5.93269560e+00, 7.40194410e+00, 9.97056077e+00
Function Value: 6.81768257e+03
Step: -1.85873488e+00, -1.57763016e+00, -2.29685392e-02
Gradient: 2.50574829e+03, 1.62217384e+03, 1.99411215e+01
Norm of Step: 2.43810169e+00
Norm of Gradient: 2.98506618e+03
Iteration 15
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Design Variables: 4.00000000e+00, 4.97162389e+00, 8.30990496e+00
Function Value: 1.44798679e+03
Step: -1.93269560e+00, -2.43032021e+00, -1.66065581e+00
Gradient: 7.68000000e+02, 4.91535388e+02, 1.66198099e+01
Norm of Step: 3.52129895e+00
Norm of Gradient: 9.11979855e+02
KKT conditions are satisfied for box constrained problem
Iteration 16
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Design Variables: 4.00000000e+00, 4.00000000e+00, 1.77635684e-15
Function Value: 1.02400000e+03
Step: 0.00000000e+00, -9.71623890e-01, -8.30990496e+00
Gradient: 7.68000000e+02, 2.56000000e+02, 3.55271368e-15
Norm of Step: 8.36651501e+00
Norm of Gradient: 8.09543081e+02
Optimization required 17 function/gradient evaluations
Trust-region produced [4.0000000e+00,4.0000000e+00,1.7763568e-15)
Value of F(X) = 1.0240000e+03
---------------------------------------------------------
Running testcase_11 as least squares problem:
Exact solution (0, 0, 0)
---------------------------------------------------------
Gradient is within tolerance, x likely a local optimum.
Optimization required 17 function/gradient evaluations
Gauss-Newton produced (1.52588e-04,1.52588e-04,0.00000e+00)
Norm of RES(X) = 7.3627514e-08