===================================================================== ===================================================================== ===================================================================== ===================================================================== RESULTS WITH THE BPK-BASED MDMt FACTORIZATION RESULTS WITH THE SPECTRAL-QDQt-BASED MDMt FACTORIZATION ===================================================================== ===================================================================== ===================================================================== ===================================================================== Parameter: eps = 1.0000000000000000E-008 Parameter: eps = 1.0000000000000000E-008 STOP = 0: xk is such that |g(xk)|xlarge, with xlarge=1.0d+10. STOP = 10: xk is such that |x|>xlarge, with xlarge=1.0d+10. STOP = 11: the maximum allowed number of iterations was exhausted (maxit = 500000 ). STOP = 11: the maximum allowed number of iterations was exhausted (maxit = 500000 ). STOP = 12: the maximum allowed number of functional evaluations was exhausted (maxfcnt = 5000000 ). STOP = 12: the maximum allowed number of functional evaluations was exhausted (maxfcnt = 5000000 ). STOP = -90: xk is such that there was an error in the evaluation of the objective function. STOP = -90: xk is such that there was an error in the evaluation of the objective function. STOP = -91: xk is such that there was an error in the evaluation of the gradient. STOP = -91: xk is such that there was an error in the evaluation of the gradient. STOP = -92: xk is such that there was an error in the evaluation of the Hessian. STOP = -92: xk is such that there was an error in the evaluation of the Hessian. Each problem was run ntimes times, where ntimes is such that the CPU time for the ntimes runs is larger Each problem was run ntimes times, where ntimes is such that the CPU time for the ntimes runs is larger not smaller than a second. Assuming that the time is measured with a precision of at least 0.01 seconds, the not smaller than a second. Assuming that the time is measured with a precision of at least 0.01 seconds, the time for the ntimes runs has an error smaller than 1%. The reported time is the average of the ntimes runs. time for the ntimes runs has an error smaller than 1%. The reported time is the average of the ntimes runs. **************** **************** STARTING FROM x0 STARTING FROM x0 **************** **************** --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- Problem n m f |g| iter fcnt time STOP Problem n m f |g| iter fcnt time STOP --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- 1 Rosenbrock 2 2 1.2449211161D-30 4.4D-14 21 28 0.000309 0 1 Rosenbrock 2 2 6.9602611535D-20 9.5D-09 21 29 0.000309 0 2 Freudenstein and Roth 2 2 4.8984253679D+01 2.8D-14 7 8 0.000094 4 2 Freudenstein and Roth 2 2 4.8984253679D+01 5.7D-14 7 8 0.000093 4 3 Powell badly scaled 2 2 8.6435107281D-26 4.2D-09 99 134 0.001527 0 3 Powell badly scaled 2 2 8.7741658155D-26 4.2D-09 99 134 0.001543 0 4 Brown badly scaled 2 3 0.0000000000D+00 0.0D+00 9 12 0.000132 0 4 Brown badly scaled 2 3 0.0000000000D+00 0.0D+00 9 12 0.000131 0 5 Beale 2 3 3.7717412031D-29 8.0D-15 7 8 0.000098 0 5 Beale 2 3 9.0787881518D-26 1.3D-12 9 10 0.000127 0 6 Jennrich and Sampson 2 10 1.2436218236D+02 2.0D-12 10 11 0.000152 0 6 Jennrich and Sampson 2 10 1.2436218236D+02 2.0D-12 10 11 0.000151 0 7 Helical valley 3 3 1.7541356084D-37 2.0D-18 16 20 0.000253 0 7 Helical valley 3 3 2.2697109414D-22 3.0D-10 16 21 0.000275 0 8 Bard 3 15 8.2148773066D-03 3.5D-09 12 15 0.000211 0 8 Bard 3 15 8.2148773066D-03 2.6D-13 10 12 0.000188 0 9 Gaussian 3 15 1.1279327696D-08 8.4D-11 2 3 0.000036 0 9 Gaussian 3 15 1.1279327696D-08 8.4D-11 2 3 0.000037 0 10 Meyer 3 16 8.7945855963D+01 1.4D+05 184 272 0.003702 6 10 Meyer 3 16 8.7945855282D+01 5.2D+05 181 276 0.003883 6 11 Gulf research and development 3 10 3.8500000000D-02 0.0D+00 1 2 0.000023 0 11 Gulf research and development 3 10 3.8500000000D-02 0.0D+00 1 2 0.000025 0 12 Box three-dimensional 3 10 1.1096184229D-19 1.8D-10 30 34 0.000514 0 12 Box three-dimensional 3 10 2.2646150481D-26 8.8D-14 15 17 0.000272 0 13 Powell singular 4 4 1.3168161721D-12 8.7D-09 20 21 0.000332 0 13 Powell singular 4 4 1.3168161722D-12 8.7D-09 20 21 0.000386 0 14 Wood 4 6 5.9656373362D-29 2.2D-13 39 52 0.000654 0 14 Wood 4 6 1.8032603202D-22 1.6D-10 38 52 0.000737 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 4.4D-13 8 12 0.000160 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 3.6D-14 8 12 0.000177 0 16 Brown and Dennis 4 20 8.5822201626D+04 2.9D-10 8 9 0.000170 0 16 Brown and Dennis 4 20 8.5822201626D+04 3.2D-10 8 9 0.000183 0 17 Osborne 1 5 33 5.4648946975D-05 2.1D-09 66 84 0.001648 0 17 Osborne 1 5 33 5.4648946975D-05 9.8D-14 44 69 0.001343 0 18 Biggs EXP6 6 13 4.1150709175D-21 1.4D-10 34 42 0.000788 0 18 Biggs EXP6 6 13 2.4267686987D-01 5.6D-04 3077 3934 0.084022 2 19 Osborne 2 11 65 8.7594724093D-02 8.2D-10 28 38 0.001576 0 19 Osborne 2 11 65 4.0137736294D-02 2.4D-09 19 22 0.001339 0 20 Watson 31 31 3.9935634747D-10 9.9D-09 17 18 0.003160 0 20 Watson 31 31 1.3796102845D-10 5.5D-09 15 16 0.004678 0 21 Extended Rosenbrock 10 10 6.2246055803D-30 4.4D-14 21 28 0.000459 0 21 Extended Rosenbrock 10 10 3.4801305768D-19 9.5D-09 21 29 0.000488 0 22 Extended Powell singular 12 12 3.9504485164D-12 8.7D-09 20 21 0.000454 0 22 Extended Powell singular 12 12 3.9504485168D-12 8.7D-09 20 21 0.000602 0 23 Penalty I 4 5 2.2499775009D-05 8.8D-12 34 53 0.000623 0 23 Penalty I 4 5 2.2499775009D-05 4.9D-12 34 51 0.000657 0 24 Penalty II 4 8 9.3762930074D-06 3.3D-11 109 165 0.002054 0 24 Penalty II 4 8 9.3762930116D-06 8.4D-09 105 160 0.002093 0 25 Variably dimensioned 10 12 1.7470729905D-26 2.6D-12 14 15 0.000289 0 25 Variably dimensioned 10 12 1.7470729905D-26 2.6D-12 14 15 0.000414 0 26 Trigonometric 10 10 2.7950561219D-05 2.2D-09 11 15 0.000287 0 26 Trigonometric 10 10 2.7950561219D-05 2.9D-12 11 14 0.000442 0 27 Brown almost-linear 40 40 1.2789059618D-20 7.6D-11 11 12 0.000787 0 27 Brown almost-linear 40 40 3.8168572676D-25 8.7D-14 11 12 0.003228 0 28 Discrete boundary value 10 10 1.8574478838D-24 1.9D-13 3 4 0.000069 0 28 Discrete boundary value 10 10 1.8574917908D-24 1.9D-13 3 4 0.000108 0 29 Discrete integral equation 10 10 3.9940999324D-22 2.7D-11 3 4 0.000082 0 29 Discrete integral equation 10 10 3.9940999324D-22 2.7D-11 3 4 0.000121 0 30 Broyden tridiagonal 10 10 1.2818989710D-30 9.1D-15 6 7 0.000126 0 30 Broyden tridiagonal 10 10 1.3928325358D-30 1.1D-14 6 7 0.000209 0 31 Broyden banded 10 10 1.2095976349D-26 1.0D-12 8 9 0.000187 0 31 Broyden banded 10 10 1.2109366955D-26 1.0D-12 8 9 0.000290 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000017 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000017 0 33 Linear - rank 1 10 10 2.1428571429D+00 3.1D-11 6 7 0.000120 0 33 Linear - rank 1 10 10 2.1428571429D+00 3.9D-12 2 3 0.000063 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 1.1D-11 1 2 0.000019 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 4.2D-12 2 3 0.000056 0 35 Chebyquad 8 8 3.5168737257D-03 2.0D-12 12 19 0.000296 0 35 Chebyquad 8 8 3.5168737257D-03 1.1D-15 11 16 0.000341 0 ******************* ******************* STARTING FROM 10 x0 STARTING FROM 10 x0 ******************* ******************* --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- Problem n m f |g| iter fcnt time STOP Problem n m f |g| iter fcnt time STOP --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- 1 Rosenbrock 2 2 3.9486989177D-21 1.1D-09 58 91 0.000892 0 1 Rosenbrock 2 2 2.3418371393D-18 3.0D-09 57 91 0.000867 0 2 Freudenstein and Roth 2 2 4.8984253679D+01 5.7D-14 17 18 0.000238 0 2 Freudenstein and Roth 2 2 4.8984253679D+01 8.5D-14 17 18 0.000223 4 3 Powell badly scaled 2 2 1.0201602030D-08 1.3D-02 6745 12963 0.125024 3 3 Powell badly scaled 2 2 1.0201607900D-08 1.3D-02 6748 12986 0.123374 3 4 Brown badly scaled 2 3 1.9721522631D-31 8.9D-10 29 49 0.000500 0 4 Brown badly scaled 2 3 0.0000000000D+00 0.0D+00 32 45 0.000489 0 5 Beale 2 3 2.2559506512D-17 3.6D-09 46 51 0.000685 0 5 Beale 2 3 2.0058676589D-20 1.2D-09 46 55 0.000679 0 6 Jennrich and Sampson 2 10 1.2436218236D+02 1.8D-12 83 84 0.001284 0 6 Jennrich and Sampson 2 10 1.2436218236D+02 1.8D-12 83 84 0.001235 0 7 Helical valley 3 3 1.9417332323D-20 2.7D-09 17 22 0.000286 0 7 Helical valley 3 3 7.5912671499D-33 4.2D-16 18 24 0.000302 0 8 Bard 3 15 8.2148773066D-03 7.8D-11 16 18 0.000275 0 8 Bard 3 15 8.2148773066D-03 7.5D-10 17 28 0.000352 0 9 Gaussian 3 15 5.6422337000D-01 8.2D-16 2 3 0.000038 0 9 Gaussian 3 15 5.6422337000D-01 5.5-188 2 3 0.000040 0 10 Meyer 3 16 1.5683472916D+07 6.2D-02 23414 46777 0.542964 3 10 Meyer 3 16 3.5540174818D+08 2.4D+06 82 637 0.004085 -90 11 Gulf research and development 3 10 1.1943774921D-32 2.6D-16 0 1 0.000004 0 11 Gulf research and development 3 10 1.1943774921D-32 2.6D-16 0 1 0.000004 0 12 Box three-dimensional 3 10 7.1162461522D-23 1.3D-11 46 54 0.000824 0 12 Box three-dimensional 3 10 1.8616215905D-22 7.7D-12 47 53 0.000875 0 13 Powell singular 4 4 7.8223083987D-13 5.9D-09 26 27 0.000432 0 13 Powell singular 4 4 7.8223083989D-13 5.9D-09 26 27 0.000497 0 14 Wood 4 6 3.1715627535D-24 1.4D-11 44 57 0.000765 0 14 Wood 4 6 1.3570872760D-30 4.4D-14 44 57 0.000833 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 1.7D-10 26 33 0.000514 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 4.8D-09 28 39 0.000601 0 16 Brown and Dennis 4 20 8.5822201626D+04 2.3D-10 14 15 0.000297 0 16 Brown and Dennis 4 20 8.5822201626D+04 2.3D-10 14 15 0.000314 0 17 Osborne 1 5 33 4.6727569525D-02 1.2D-02 305591 468782 8.408005 8 17 Osborne 1 5 33 4.6847574236D-02 8.1D-05 80878 99264 2.382282 8 18 Biggs EXP6 6 13 6.2951164948D-26 3.5D-13 105 146 0.002380 0 18 Biggs EXP6 6 13 7.3417189522D-20 2.3D-11 117 178 0.003286 0 19 Osborne 2 11 65 1.7898135869D+00 7.8D-15 8 14 0.000402 0 19 Osborne 2 11 65 1.7898135869D+00 6.7D-16 9 14 0.000460 0 20 Watson 31 31 3.2949820370D-07 8.7D-09 119 143 0.022967 0 20 Watson 31 31 4.0775926087D-08 6.9D-09 182 223 0.056694 0 21 Extended Rosenbrock 10 10 1.9743494588D-20 1.1D-09 58 91 0.001334 0 21 Extended Rosenbrock 10 10 1.1709185696D-17 3.0D-09 57 91 0.001374 0 22 Extended Powell singular 12 12 2.3466925196D-12 5.9D-09 26 27 0.000578 0 22 Extended Powell singular 12 12 2.3466925198D-12 5.9D-09 26 27 0.000772 0 23 Penalty I 4 5 2.2499775009D-05 1.6D-10 39 54 0.000652 0 23 Penalty I 4 5 2.2499775009D-05 2.5D-09 39 55 0.000721 0 24 Penalty II 4 8 9.3762930074D-06 4.7D-09 114 170 0.002053 0 24 Penalty II 4 8 9.3762930074D-06 1.4D-09 110 154 0.002123 0 25 Variably dimensioned 10 12 0.0000000000D+00 0.0D+00 17 18 0.000364 0 25 Variably dimensioned 10 12 0.0000000000D+00 0.0D+00 17 18 0.000533 0 26 Trigonometric 10 10 4.2186338879D-05 3.0D-12 19 24 0.000467 0 26 Trigonometric 10 10 4.2186338879D-05 3.7D-13 17 20 0.000650 0 27 Brown almost-linear 40 40 9.9999999993D-01 1.4D-10 55 185 0.005258 0 27 Brown almost-linear 40 40 1.0000000000D+00 4.1D-13 1377 3369 0.476614 0 28 Discrete boundary value 10 10 6.2535013544D-21 1.1D-11 5 6 0.000114 0 28 Discrete boundary value 10 10 6.2535035078D-21 1.1D-11 5 6 0.000177 0 29 Discrete integral equation 10 10 5.7162263950D-18 3.5D-09 5 6 0.000137 0 29 Discrete integral equation 10 10 5.7162263950D-18 3.5D-09 5 6 0.000202 0 30 Broyden tridiagonal 10 10 3.1769123383D-21 2.0D-10 11 12 0.000223 0 30 Broyden tridiagonal 10 10 3.1769107132D-21 2.0D-10 11 12 0.000388 0 31 Broyden banded 10 10 7.6806086182D-30 2.5D-14 18 19 0.000384 0 31 Broyden banded 10 10 7.6806086182D-30 2.5D-14 18 19 0.000666 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000018 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000017 0 33 Linear - rank 1 10 10 2.1428571429D+00 6.9D-10 6 7 0.000125 0 33 Linear - rank 1 10 10 2.1428571429D+00 8.6D-11 2 3 0.000063 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 3.7D-11 1 2 0.000019 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 1.5D-11 2 3 0.000056 0 35 Chebyquad 8 8 3.5168737257D-03 3.1D-13 79 88 0.001667 0 35 Chebyquad 8 8 3.5168737257D-03 2.6D-13 83 96 0.002471 0 ******************** ******************** STARTING FROM 100 x0 STARTING FROM 100 x0 ******************** ******************** --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- Problem n m f |g| iter fcnt time STOP Problem n m f |g| iter fcnt time STOP --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- 1 Rosenbrock 2 2 3.8770992834D-20 1.4D-09 236 359 0.003818 0 1 Rosenbrock 2 2 4.5242268692D-25 2.5D-11 235 362 0.003612 0 2 Freudenstein and Roth 2 2 4.8984253679D+01 5.7D-14 27 28 0.000369 0 2 Freudenstein and Roth 2 2 4.8984253679D+01 5.7D-14 27 28 0.000355 0 3 Powell badly scaled 2 2 1.0099697577D-08 1.6D-03 1006 2008 0.019797 2 3 Powell badly scaled 2 2 1.0099697577D-08 1.6D-03 1006 2008 0.018520 2 4 Brown badly scaled 2 3 0.0000000000D+00 0.0D+00 24 34 0.000384 0 4 Brown badly scaled 2 3 0.0000000000D+00 0.0D+00 25 31 0.000369 0 5 Beale 2 3 5.9288848983D-24 7.0D-12 109 142 0.001618 0 5 Beale 2 3 3.9443045261D-31 5.3D-15 109 143 0.001658 0 6 Jennrich and Sampson 2 10 Infinity 7.0D-12 0 1 0.000001 -90 6 Jennrich and Sampson 2 10 Infinity 5.3D-15 0 1 0.000001 -90 7 Helical valley 3 3 3.6211405706D-24 3.8D-11 14 19 0.000212 0 7 Helical valley 3 3 3.8489397621D-33 3.0D-16 16 23 0.000274 0 8 Bard 3 15 8.2148773066D-03 4.2D-11 20 30 0.000367 0 8 Bard 3 15 8.2148773066D-03 6.9D-15 23 39 0.000485 0 9 Gaussian 3 15 5.6422337000D-01 0.0D+00 1 2 0.000020 0 9 Gaussian 3 15 5.6422337000D-01 0.0D+00 1 2 0.000022 0 10 Meyer 3 16 1.5683494924D+07 6.2D-02 23425 46785 0.512127 3 10 Meyer 3 16 1.5683498146D+07 6.2D-02 23424 46782 0.552889 3 11 Gulf research and development 3 10 3.8500000000D-02 0.0D+00 0 1 0.000003 0 11 Gulf research and development 3 10 3.8500000000D-02 0.0D+00 0 1 0.000003 0 12 Box three-dimensional 3 10 7.5588740755D-02 2.1D-13 39 46 0.000662 0 12 Box three-dimensional 3 10 7.5588740755D-02 7.9D-10 26 33 0.000465 0 13 Powell singular 4 4 4.6467008818D-13 4.0D-09 32 33 0.000512 0 13 Powell singular 4 4 4.6467008820D-13 4.0D-09 32 33 0.000588 0 14 Wood 4 6 1.5259230340D-25 8.0D-12 46 62 0.000863 0 14 Wood 4 6 2.1395386864D-28 4.1D-13 46 61 0.000871 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 3.7D-10 75 115 0.001569 0 15 Kowalik and Osborne 4 11 3.0750560385D-04 1.2D-13 80 116 0.001753 0 16 Brown and Dennis 4 20 8.5822201626D+04 8.7D-11 20 21 0.000435 0 16 Brown and Dennis 4 20 8.5822201626D+04 3.0D-10 20 35 0.000525 0 17 Osborne 1 5 33 7.9756992747D-05 1.7D-09 53 78 0.001442 0 17 Osborne 1 5 33 7.9775500364D-05 3.6D-09 50 78 0.001491 0 18 Biggs EXP6 6 13 5.6556497000D-03 2.3D-11 110 132 0.002743 0 18 Biggs EXP6 6 13 5.6556494274D-03 5.0D-11 93 113 0.002544 0 19 Osborne 2 11 65 1.7898135869D+00 9.8D-11 15 26 0.000780 0 19 Osborne 2 11 65 1.7898135869D+00 6.7D-16 15 25 0.000784 0 20 Watson 31 31 1.6865884004D-05 6.1D-08 162 169 0.030931 1 20 Watson 31 31 3.5928644382D-06 2.5D-08 317 374 0.098425 1 21 Extended Rosenbrock 10 10 1.9376502655D-19 1.4D-09 236 359 0.005728 0 21 Extended Rosenbrock 10 10 8.3529353544D-24 1.6D-12 235 363 0.005600 0 22 Extended Powell singular 12 12 1.3940102645D-12 4.0D-09 32 33 0.000728 0 22 Extended Powell singular 12 12 1.3940102646D-12 4.0D-09 32 33 0.000942 0 23 Penalty I 4 5 2.2499775009D-05 5.5D-10 44 59 0.000761 0 23 Penalty I 4 5 2.2499775009D-05 4.0D-10 43 57 0.000795 0 24 Penalty II 4 8 9.3762930101D-06 3.8D-09 116 166 0.002086 0 24 Penalty II 4 8 9.3762930074D-06 9.1D-09 118 169 0.002316 0 25 Variably dimensioned 10 12 7.0625390991D-22 5.3D-10 23 24 0.000495 0 25 Variably dimensioned 10 12 7.0625390991D-22 5.3D-10 23 24 0.000692 0 26 Trigonometric 10 10 2.7950561219D-05 7.4D-11 16 19 0.000390 0 26 Trigonometric 10 10 2.7950561219D-05 1.4D-12 16 17 0.000625 0 27 Brown almost-linear 40 40 1.0000000000D+00 9.9D-11 43 572 0.007203 0 27 Brown almost-linear 40 40 9.3140598636D+04 3.9D+49 257 13425 0.232221 9 28 Discrete boundary value 10 10 6.8422991619D-21 1.2D-11 14 15 0.000301 0 28 Discrete boundary value 10 10 6.8422978642D-21 1.2D-11 14 15 0.000487 0 29 Discrete integral equation 10 10 1.8068824367D-27 5.6D-14 14 15 0.000344 0 29 Discrete integral equation 10 10 2.5069642886D-26 2.5D-13 14 15 0.000559 0 30 Broyden tridiagonal 10 10 8.8710860059D-27 3.5D-13 17 18 0.000347 0 30 Broyden tridiagonal 10 10 8.8374115060D-27 3.5D-13 17 18 0.000601 0 31 Broyden banded 10 10 2.2289135532D-25 4.4D-12 28 29 0.000580 0 31 Broyden banded 10 10 2.2289135532D-25 4.4D-12 28 29 0.001000 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000017 0 32 Linear - full rank 10 10 0.0000000000D+00 0.0D+00 1 2 0.000017 0 33 Linear - rank 1 10 10 2.1428571429D+00 5.0D-09 6 7 0.000113 0 33 Linear - rank 1 10 10 2.1428571429D+00 6.3D-10 2 3 0.000066 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 1.1D-09 1 2 0.000018 0 34 Linear - rank 1 with zero colu 10 10 3.6470588235D+00 3.8D-10 2 3 0.000058 0 35 Chebyquad 8 8 3.5168737257D-03 3.4D-11 112 122 0.002347 0 35 Chebyquad 8 8 3.5168737257D-03 4.5D-09 116 130 0.003512 0 ************************************************* ************************************************* PROBLEMS WITH VARIABLE DIMENSION STARTING FROM x0 PROBLEMS WITH VARIABLE DIMENSION STARTING FROM x0 ************************************************* ************************************************* --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- Problem n m f |g| iter fcnt time STOP Problem n m f |g| iter fcnt time STOP --------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------- 21 Extended Rosenbrock 1000 1000 6.2246055803D-28 4.4D-14 21 28 2.142597 0 21 Extended Rosenbrock 1000 1000 3.4801305768D-17 9.5D-09 21 29 12.522365 0 22 Extended Powell singular 1000 1000 3.2920404303D-10 8.7D-09 20 21 2.119298 0 22 Extended Powell singular 1000 1000 3.2920404307D-10 8.7D-09 20 21 11.962153 0 23 Penalty I 1000 1001 9.6861754324D-03 2.4D-13 41 51 4.259248 0 23 Penalty I 1000 1001 9.6861754327D-03 4.8D-09 40 50 33.979084 0 24 Penalty II 1000 2000 3.1508238116D+82 1.9D+67 274 4391 29.594519 8 24 Penalty II 1000 2000 8.8037683088D+82 5.1D+67 35 2339 59.991001 8 25 Variably dimensioned 1000 1002 0.0000000000D+00 0.0D+00 37 38 3.828147 0 25 Variably dimensioned 1000 1002 0.0000000000D+00 0.0D+00 37 38 52.442870 0 26 Trigonometric 1000 1000 1.4366645521D-07 5.3D-09 278 362 29.135424 0 26 Trigonometric 1000 1000 1.7818178809D-08 1.7D-10 15 20 28.801061 0 27 Brown almost-linear 1000 1000 1.0000000000D+00 5.3D-09 1 2 0.436061 0 27 Brown almost-linear 1000 1000 2.4614483263D-13 1.2D-09 2 4 2.858946 0 28 Discrete boundary value 1000 1000 7.2153535917D-13 1.6D-12 1 2 0.119425 0 28 Discrete boundary value 1000 1000 6.0704127198D-10 6.0D-11 1 3 1.762774 0 29 Discrete integral equation 1000 1000 2.9699073236D-20 2.5D-11 3 4 3.677467 0 29 Discrete integral equation 1000 1000 2.9699073746D-20 2.5D-11 3 4 8.946682 0 30 Broyden tridiagonal 1000 1000 8.4802547311D-30 1.2D-14 6 7 0.579685 0 30 Broyden tridiagonal 1000 1000 1.0057976542D-29 1.5D-14 6 7 14.142467 0 31 Broyden banded 1000 1000 1.2209090837D-26 1.0D-12 8 9 0.772367 0 31 Broyden banded 1000 1000 1.2208559281D-26 1.0D-12 8 9 14.899365 0 32 Linear - full rank 1000 1000 0.0000000000D+00 0.0D+00 1 2 0.097838 0 32 Linear - full rank 1000 1000 0.0000000000D+00 0.0D+00 1 2 0.613405 0 33 Linear - rank 1 1000 1000 2.4962518741D+02 2.7D+01 7 12 0.798017 6 33 Linear - rank 1 1000 1000 2.4962518741D+02 2.7D-01 6 23 9.735447 6 34 Linear - rank 1 with zero colu 1000 1000 2.5112518778D+02 1.7D+01 4 6 0.489679 7 34 Linear - rank 1 with zero colu 1000 1000 2.5112518778D+02 8.8D+00 3 4 4.915662 7 35 Chebyquad 400 400 9.2207094953D-03 8.6D-12 939 1225 95.281571 0 35 Chebyquad 400 400 8.3808239886D-03 6.0D-12 87 116 18.756403 0