Thu Feb 12 19:11:42 2026 test_opt_test(): python version: 3.10.12 numpy version: 1.26.4 Test test_opt(). p00_title_test(): p00_title() prints the title for any problem. Problem Title 1 "The Fletcher-Powell helical valley function." 2 "The Biggs EXP6 function." 3 "The Gaussian function." 4 "The Powell badly scaled function." 5 "The Box 3-dimensional function." 6 "The variably dimensioned function." 7 "The Watson function." 8 "The Penalty Function #1." 9 "The Penalty Function #2." 10 "The Brown Badly Scaled Function." 11 "The Brown and Dennis Function." 12 "The Gulf R&D Function." 13 "The Trigonometric Function." 14 "The Extended Rosenbrock parabolic valley Function." 15 "The Extended Powell Singular Quartic Function." 16 "The Beale Function." 17 "The Wood Function." 18 "The Chebyquad Function" 19 "The Leon cubic valley function" 20 "The Gregory and Karney Tridiagonal Matrix Function" 21 "The Hilbert Matrix Function F = x'Ax" 22 "The De Jong Function F1" 23 "The De Jong Function F2" 24 "The De Jong Function F3, (discontinuous)" 25 "The De Jong Function F4 (with Gaussian noise)" 26 "The De Jong Function F5" 27 "The Schaffer Function F6" 28 "The Schaffer Function F7" 29 "The Goldstein Price Polynomial" 30 "The Branin RCOS Function" 31 "The Shekel SQRN5 Function" 32 "The Shekel SQRN7 Function" 33 "The Shekel SQRN10 Function" 34 "The Six-Hump Camel-Back Polynomial" 35 "The Shubert Function" 36 "The Himmelblau function." 37 "The Easom Function" 38 "The Bohachevsky Function #1" 39 "The Bohachevsky Function #2" 40 "The Bohachevsky Function #3" 41 "The Colville Polynomial" 42 "The Powell 3D Function" 43 "The Himmelblau function." p00_n_test(): p00_n() returns problem size or a minimum problem size. 1 3 2 6 3 3 4 2 5 3 6 1 (minimum) 7 2 (minimum) 8 1 (minimum) 9 1 (minimum) 10 2 11 4 12 3 13 1 (minimum) 14 1 (minimum) 15 4 (minimum) 16 2 17 4 18 1 (minimum) 19 2 20 1 (minimum) 21 1 (minimum) 22 3 23 2 24 5 25 30 26 2 27 2 28 2 29 2 30 2 31 4 32 4 33 4 34 2 35 2 36 2 37 2 38 2 39 2 40 2 41 4 42 3 43 2 p00_start_test(): p00_start() provides a starting point for minimization. 1: "The Fletcher-Powell helical valley function." array([-1., 0., 0.]) 2: "The Biggs EXP6 function." array([1., 2., 1., 1., 1., 1.]) 3: "The Gaussian function." array([0.4, 1. , 0. ]) 4: "The Powell badly scaled function." array([0., 1.]) 5: "The Box 3-dimensional function." array([ 0., 10., 5.]) 6: "The variably dimensioned function." array([0.75, 0.5 , 0.25, 0. ]) 7: "The Watson function." array([0., 0., 0., 0.]) 8: "The Penalty Function #1." array([1., 2., 3., 4.]) 9: "The Penalty Function #2." array([0.5, 0.5, 0.5, 0.5]) 10: "The Brown Badly Scaled Function." array([1., 1.]) 11: "The Brown and Dennis Function." array([25., 5., -5., -1.]) 12: "The Gulf R&D Function." array([40. , 20. , 1.2]) 13: "The Trigonometric Function." array([0.25, 0.25, 0.25, 0.25]) 14: "The Extended Rosenbrock parabolic valley Function." array([-1.2, 1. , -1.2, 1. ]) 15: "The Extended Powell Singular Quartic Function." array([ 3., -1., 0., 1.]) 16: "The Beale Function." array([1., 1.]) 17: "The Wood Function." array([-3., -1., -3., -1.]) 18: "The Chebyquad Function" array([0.2, 0.4, 0.6, 0.8]) 19: "The Leon cubic valley function" array([-1.2, -1. ]) 20: "The Gregory and Karney Tridiagonal Matrix Function" array([0., 0., 0., 0.]) 21: "The Hilbert Matrix Function F = x'Ax" array([1., 1., 1., 1.]) 22: "The De Jong Function F1" array([-5.12, 0. , 5.12]) 23: "The De Jong Function F2" array([-2.048, 2.048]) 24: "The De Jong Function F3, (discontinuous)" array([-5.12, -2.56, 0. , 2.56, 5.12]) 25: "The De Jong Function F4 (with Gaussian noise)" array([-1.28 , -1.19172414, -1.10344828, -1.01517241, -0.92689655, -0.83862069, -0.75034483, -0.66206897, -0.5737931 , -0.48551724, -0.39724138, -0.30896552, -0.22068966, -0.13241379, -0.04413793, 0.04413793, 0.13241379, 0.22068966, 0.30896552, 0.39724138, 0.48551724, 0.5737931 , 0.66206897, 0.75034483, 0.83862069, 0.92689655, 1.01517241, 1.10344828, 1.19172414, 1.28 ]) 26: "The De Jong Function F5" array([-32.01, -32.02]) 27: "The Schaffer Function F6" array([-5., 10.]) 28: "The Schaffer Function F7" array([-5., 10.]) 29: "The Goldstein Price Polynomial" array([-0.5 , 0.25]) 30: "The Branin RCOS Function" array([-1., 1.]) 31: "The Shekel SQRN5 Function" array([1., 3., 5., 6.]) 32: "The Shekel SQRN7 Function" array([1., 3., 5., 6.]) 33: "The Shekel SQRN10 Function" array([1., 3., 5., 6.]) 34: "The Six-Hump Camel-Back Polynomial" array([-1.5, 0.5]) 35: "The Shubert Function" array([0.5, 1. ]) 36: "The Himmelblau function." array([-1.3, 2.7]) 37: "The Easom Function" array([0.5, 1. ]) 38: "The Bohachevsky Function #1" array([0.5, 1. ]) 39: "The Bohachevsky Function #2" array([0.6, 1.3]) 40: "The Bohachevsky Function #3" array([0.5, 1. ]) 41: "The Colville Polynomial" array([ 0.5, 1. , -0.5, -1. ]) 42: "The Powell 3D Function" array([0., 1., 2.]) 43: "The Himmelblau function." array([-1.3, 2.7]) p00_f_test(): p00_f() evaluates the objective function F(X). In this test, we evaluate F at a typical starting point. 1: "The Fletcher-Powell helical valley function." f(x_start) = 2500.0 2: "The Biggs EXP6 function." f(x_start) = 0.7790700756559702 3: "The Gaussian function." f(x_start) = 0.0685525406311173 4: "The Powell badly scaled function." f(x_start) = 1.1352617173483783 5: "The Box 3-dimensional function." f(x_start) = 34.732488161400184 6: "The variably dimensioned function." f(x_start) = 3222.1875 7: "The Watson function." f(x_start) = 30.0 8: "The Penalty Function #1." f(x_start) = 885.06264 9: "The Penalty Function #2." f(x_start) = 2.3400088054630244 10: "The Brown Badly Scaled Function." f(x_start) = 999998000003.0 11: "The Brown and Dennis Function." f(x_start) = 7926693.336997435 12: "The Gulf R&D Function." f(x_start) = 1.2053838794073308 13: "The Trigonometric Function." f(x_start) = 0.013053127851381652 14: "The Extended Rosenbrock parabolic valley Function." f(x_start) = 48.39999999999999 15: "The Extended Powell Singular Quartic Function." f(x_start) = 215.0 16: "The Beale Function." f(x_start) = 14.203125 17: "The Wood Function." f(x_start) = 19192.0 18: "The Chebyquad Function" f(x_start) = 0.07118392888888889 19: "The Leon cubic valley function" f(x_start) = 57.8384 20: "The Gregory and Karney Tridiagonal Matrix Function" f(x_start) = 0.0 21: "The Hilbert Matrix Function F = x'Ax" f(x_start) = 5.076190476190478 22: "The De Jong Function F1" f(x_start) = 52.4288 23: "The De Jong Function F2" f(x_start) = 469.9523900415999 24: "The De Jong Function F3, (discontinuous)" f(x_start) = -2.0 25: "The De Jong Function F4 (with Gaussian noise)" f(x_start) = 284.84304906748457 26: "The De Jong Function F5" f(x_start) = 0.001999999999629697 27: "The Schaffer Function F6" f(x_start) = 0.8683937850908159 28: "The Schaffer Function F7" f(x_start) = 4.563758239636366 29: "The Goldstein Price Polynomial" f(x_start) = 2738.7433013916016 30: "The Branin RCOS Function" f(x_start) = 60.356308294938096 31: "The Shekel SQRN5 Function" f(x_start) = -0.167128036847102 32: "The Shekel SQRN7 Function" f(x_start) = -0.21514367838792342 33: "The Shekel SQRN10 Function" f(x_start) = -0.2709847141369527 34: "The Six-Hump Camel-Back Polynomial" f(x_start) = 0.6656249999999986 35: "The Shubert Function" f(x_start) = -3.1044209149932107 36: "The Himmelblau function." f(x_start) = 44.71219999999999 37: "The Easom Function" f(x_start) = -4.503563650592924e-06 38: "The Bohachevsky Function #1" f(x_start) = 2.55 39: "The Bohachevsky Function #2" f(x_start) = 4.236352549156242 40: "The Bohachevsky Function #3" f(x_start) = 3.55 41: "The Colville Polynomial" f(x_start) = 239.775 42: "The Powell 3D Function" f(x_start) = 2.4999998874648255 43: "The Himmelblau function." f(x_start) = 44.71219999999999 p00_sol_test(): p00_sol() returns a minimizing solution. Print the value of f(x) there. 1: "The Fletcher-Powell helical valley function." f(x_start) = 2500.0 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 2: "The Biggs EXP6 function." f(x_start) = 0.7790700756559702 f(x_sol) = 1.449262283151395e-32 ||f'(x_sol)|| 1.8180274942663133e-16 3: "The Gaussian function." f(x_start) = 0.0685525406311173 x_sol not given. 4: "The Powell badly scaled function." f(x_start) = 1.1352617173483783 f(x_sol) = 1.4552592950009715e-13 ||f'(x_sol)|| 0.0694759967078489 5: "The Box 3-dimensional function." f(x_start) = 34.732488161400184 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 6: "The variably dimensioned function." f(x_start) = 3222.1875 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 7: "The Watson function." f(x_start) = 30.0 f(x_sol) = 0.002287670069769948 ||f'(x_sol)|| 8.736682679655731e-05 8: "The Penalty Function #1." f(x_start) = 885.06264 x_sol not given. 9: "The Penalty Function #2." f(x_start) = 2.3400088054630244 x_sol not given. 10: "The Brown Badly Scaled Function." f(x_start) = 999998000003.0 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 11: "The Brown and Dennis Function." f(x_start) = 7926693.336997435 f(x_sol) = 85822.35415219344 ||f'(x_sol)|| 37.877197155280115 12: "The Gulf R&D Function." f(x_start) = 1.2053838794073308 f(x_sol) = 8.435603249071474e-31 ||f'(x_sol)|| 7.130177410726175e-15 13: "The Trigonometric Function." f(x_start) = 0.013053127851381652 x_sol not given. 14: "The Extended Rosenbrock parabolic valley Function." f(x_start) = 48.39999999999999 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 15: "The Extended Powell Singular Quartic Function." f(x_start) = 215.0 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 16: "The Beale Function." f(x_start) = 14.203125 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 17: "The Wood Function." f(x_start) = 19192.0 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 18: "The Chebyquad Function" f(x_start) = 0.07118392888888889 f(x_sol) = 9.249617598971389e-14 ||f'(x_sol)|| 2.0289812759594104e-06 19: "The Leon cubic valley function" f(x_start) = 57.8384 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 20: "The Gregory and Karney Tridiagonal Matrix Function" f(x_start) = 0.0 f(x_sol) = -4.0 ||f'(x_sol)|| 1.0 21: "The Hilbert Matrix Function F = x'Ax" f(x_start) = 5.076190476190478 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 22: "The De Jong Function F1" f(x_start) = 52.4288 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 23: "The De Jong Function F2" f(x_start) = 469.9523900415999 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 24: "The De Jong Function F3, (discontinuous)" f(x_start) = -2.0 f(x_sol) = -25.0 ||f'(x_sol)|| 0.0 25: "The De Jong Function F4 (with Gaussian noise)" f(x_start) = 284.84304906748457 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 26: "The De Jong Function F5" f(x_start) = 0.001999999999629697 f(x_sol) = 0.0019999999996281013 ||f'(x_sol)|| 1.157177951413654e-13 27: "The Schaffer Function F6" f(x_start) = 0.8683937850908159 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 28: "The Schaffer Function F7" f(x_start) = 4.563758239636366 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 29: "The Goldstein Price Polynomial" f(x_start) = 2738.7433013916016 f(x_sol) = 3.0 ||f'(x_sol)|| 0.0 30: "The Branin RCOS Function" f(x_start) = 60.356308294938096 f(x_sol) = 0.39788735772973816 ||f'(x_sol)|| 1.175919651240861e-15 31: "The Shekel SQRN5 Function" f(x_start) = -0.167128036847102 f(x_sol) = -10.15271993245629 ||f'(x_sol)|| 0.0387847606420869 32: "The Shekel SQRN7 Function" f(x_start) = -0.21514367838792342 f(x_sol) = -10.402342918407555 ||f'(x_sol)|| 0.22044529174090632 33: "The Shekel SQRN10 Function" f(x_start) = -0.2709847141369527 f(x_sol) = -10.535807807696854 ||f'(x_sol)|| 0.224451918203128 34: "The Six-Hump Camel-Back Polynomial" f(x_start) = 0.6656249999999986 f(x_sol) = -1.0316284229280819 ||f'(x_sol)|| 0.0009224226016144319 35: "The Shubert Function" f(x_start) = -3.1044209149932107 f(x_sol) = -185.96776816075703 ||f'(x_sol)|| 82.64981640236705 36: "The Himmelblau function." f(x_start) = 44.71219999999999 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 37: "The Easom Function" f(x_start) = -4.503563650592924e-06 f(x_sol) = -1.0 ||f'(x_sol)|| 1.7319121124709866e-16 38: "The Bohachevsky Function #1" f(x_start) = 2.55 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 39: "The Bohachevsky Function #2" f(x_start) = 4.236352549156242 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 40: "The Bohachevsky Function #3" f(x_start) = 3.55 f(x_sol) = 1.0 ||f'(x_sol)|| 0.0 41: "The Colville Polynomial" f(x_start) = 239.775 f(x_sol) = 0.0 ||f'(x_sol)|| 1.4210854715202004e-14 42: "The Powell 3D Function" f(x_start) = 2.4999998874648255 f(x_sol) = 0.9999998874648253 ||f'(x_sol)|| 2.205230049456371e-06 43: "The Himmelblau function." f(x_start) = 44.71219999999999 f(x_sol) = 0.0 ||f'(x_sol)|| 0.0 p00_gdif_test(): p00_gdif() estimates the gradient vector G with a finite difference estimate GDIF Problem 1: "The Fletcher-Powell helical valley function." 1879.64 1879.64 Problem 2: "The Biggs EXP6 function." 2.5539 2.5539 Problem 3: "The Gaussian function." 0.00745153 0.320629 Problem 4: "The Powell badly scaled function." 20000.7 20000.7 Problem 5: "The Box 3-dimensional function." 26.2587 26.2587 Problem 6: "The variably dimensioned function." 9327.72 9327.72 Problem 7: "The Watson function." 104.524 104.524 Problem 8: "The Penalty Function #1." 651.79 651.79 Problem 9: "The Penalty Function #2." 16.8748 16.8748 Problem 10: "The Brown Badly Scaled Function." 2e+06 1.99885e+06 Problem 11: "The Brown and Dennis Function." 2.14049e+06 2.14049e+06 Problem 12: "The Gulf R&D Function." 5.2891 5.2891 Problem 13: "The Trigonometric Function." 0.129316 0.129316 Problem 14: "The Extended Rosenbrock parabolic valley Function." 329.325 329.325 Problem 15: "The Extended Powell Singular Quartic Function." 458.777 458.777 Problem 16: "The Beale Function." 27.75 27.75 Problem 17: "The Wood Function." 16397.1 16397.1 Problem 18: "The Chebyquad Function" 0.912348 0.912348 Problem 19: "The Leon cubic valley function" 649.911 649.911 Problem 20: "The Gregory and Karney Tridiagonal Matrix Function" 2 2 Problem 21: "The Hilbert Matrix Function F = x'Ax" 5.46502 5.46502 Problem 22: "The De Jong Function F1" 14.4815 14.4815 Problem 23: "The De Jong Function F2" 1815.82 1815.82 Problem 24: "The De Jong Function F3, (discontinuous)" 0 3.35544e+07 Problem 25: "The De Jong Function F4 (with Gaussian noise)" 389.787 389.787 Problem 26: "The De Jong Function F5" 1.15132e-13 0 Problem 27: "The Schaffer Function F6" 0.30002 0.30002 Problem 28: "The Schaffer Function F7" 4.46246 4.46246 Problem 29: "The Goldstein Price Polynomial" 16554.3 16554.3 Problem 30: "The Branin RCOS Function" 21.5043 21.5043 Problem 31: "The Shekel SQRN5 Function" 0.055138 0.055138 Problem 32: "The Shekel SQRN7 Function" 0.0674852 0.0674852 Problem 33: "The Shekel SQRN10 Function" 0.0785522 0.0785522 Problem 34: "The Six-Hump Camel-Back Polynomial" 3.87478 3.87478 Problem 35: "The Shubert Function" 51.9614 51.9614 Problem 36: "The Himmelblau function." 40.3585 40.3585 Problem 37: "The Easom Function" 2.46127e-05 2.46127e-05 Problem 38: "The Bohachevsky Function #1" 4.39767 4.39767 Problem 39: "The Bohachevsky Function #2" 4.25256 4.25256 Problem 40: "The Bohachevsky Function #3" 4.39767 4.39767 Problem 41: "The Colville Polynomial" 396.75 396.75 Problem 42: "The Powell 3D Function" 3.99732 3.99732 Problem 43: "The Himmelblau function." 40.3585 40.3585 test_opt_test(): Normal end of execution. Thu Feb 12 19:11:42 2026