Test Problem Generator for Unconstrained Global Optimization
 Computers & Operations Research, Vol. 51, pp. 338-349, 2014
by Chi-Kong Ng and Duan Li

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Note:
Version 1.0 is used in the paper
Global Descent Method for Global Optimization
SIAM Journal on Optimization Vol. 20, No. 6, pp. 3161-3184, 2010
by Chi-Kong Ng, Duan Li and Lian-Sheng Zhang
Problem Characteristics:
Problem-IDs Dimension Difficulty Level
ngli001 - ngli010 2 0
ngli011 - ngli020 1
ngli021 - ngli030 2
ngli031 - ngli040 5 0
ngli041 - ngli050 1
ngli051 - ngli060 2
ngli061 - ngli070 10 0
ngli071 - ngli080 1
ngli081 - ngli090 2
ngli091 - ngli100 20 0
ngli101 - ngli110 1
ngli111 - ngli120 2
ngli121 - ngli130 50 0
ngli131 - ngli140 1
ngli141 - ngli150 2
ngli151 - ngli160 100 0
ngli161 - ngli170 1
ngli171 - ngli180 2
ngli181 - ngli190 200 0
ngli191 - ngli200 1
ngli201 - ngli210 2
ngli211 - ngli220 500 0
ngli221 - ngli230 1
ngli231 - ngli240 2
ngli241 - ngli250 1000 0
ngli251 - ngli260 1
ngli261 - ngli270 2
ngli271 - ngli280 2000 0
ngli281 - ngli290 1
ngli291 - ngli300 2
Some Statistics:
Dimension Number of Global Minimizer Number of Non-global Minimizers Number of Saddle Points
2 1 3 4
5 1 31 210
10 1 1023 58024
20 1 2^20-1 O(3^20)
50 1 2^50-1 O(3^50)
100 1 2^100-1 O(3^100)
200 1 2^200-1 O(3^200)
500 1 2^500-1 O(3^500)
1000 1 2^1000-1 O(3^1000)
2000 1 2^2000-1 O(3^2000)
Stability Test Results:
Dimension Difficulty Level Problem-ID Norm of Gradient Minimum Eigenvalue Condition Number Local Maximum Value (fUB-fStar)/n (gUB-gStar)/n
2 0 ngli001 8.033034e-014 1.648206e+001 1.006331e+000 1.038261e+002 3.845128e+002 5.235476e+003
ngli002 9.487963e-015 5.406595e+000 1.480530e+000 5.492510e+000 1.209114e+002 4.161368e+002
ngli003 2.185910e-014 4.692839e+000 1.730659e+000 1.626172e+001 1.108541e+002 3.094715e+002
ngli004 3.535343e-014 1.395198e+001 1.075135e+000 9.754651e+001 5.623054e+002 5.544804e+003
ngli005 7.166578e-015 7.834328e+000 1.319304e+000 3.820353e+001 2.439689e+002 1.200464e+003
ngli006 4.447280e-015 1.465027e+001 1.031587e+000 6.959076e+001 3.210747e+002 5.343194e+003
ngli007 2.814196e-015 3.344952e+000 4.326030e+000 2.790738e+000 7.183051e+001 2.648495e+002
ngli008 4.035087e-014 1.655823e+001 1.159444e+000 5.714612e+000 4.400628e+002 5.415600e+002
ngli009 1.508585e-013 4.235542e+000 3.041323e+000 4.625492e+001 2.062153e+002 2.290875e+003
ngli010 1.293052e-014 5.014852e+000 1.580358e+000 1.966903e+001 1.564582e+002 1.209285e+003
1 ngli011 1.069626e-013 1.121553e+001 1.165209e+000 2.215190e+000 1.640040e+002 1.172672e+003
ngli012 4.220766e-014 5.386613e+000 3.247640e+000 4.443727e+000 1.781097e+002 3.229419e+003
ngli013 1.033859e-013 1.103280e+001 1.655471e+000 5.828355e+001 2.362629e+002 1.086648e+003
ngli014 1.241813e-014 1.059455e+001 1.156898e+000 6.346034e+001 1.462149e+002 4.105927e+003
ngli015 1.844237e-014 5.704862e+000 1.662905e+000 3.858035e+001 2.652039e+002 4.854775e+003
ngli016 3.164438e-014 3.801473e+000 8.277198e+000 7.420131e+001 1.484503e+002 2.142438e+003
ngli017 2.989577e-014 3.585651e+000 3.151705e+000 4.755454e+000 1.802743e+002 5.684283e+002
ngli018 4.975505e-014 5.849851e+000 1.249780e+000 1.429307e+001 1.309983e+002 9.098602e+002
ngli019 2.353125e-013 1.356177e+001 1.767810e+000 2.040162e+000 2.629482e+002 4.398290e+003
ngli020 8.088170e-015 8.657069e+000 2.077731e+000 3.078076e+001 2.087626e+002 5.702199e+003
2 ngli021 7.831473e-014 5.892716e+000 2.557803e+000 1.350044e+001 2.112835e+002 7.911985e+002
ngli022 2.292316e-015 5.580804e+000 3.123828e+000 1.653605e+001 1.427195e+002 2.124624e+002
ngli023 4.245982e-014 9.273238e+000 1.539450e+000 5.737945e+000 2.054733e+002 2.176066e+002
ngli024 2.410740e-014 8.406016e+000 1.477297e+000 7.410952e+001 2.856878e+002 8.928385e+002
ngli025 6.727298e-014 1.049873e+001 1.264027e+000 1.191166e+001 1.175566e+002 3.284850e+003
ngli026 1.163517e-014 7.078976e+000 1.325157e+000 7.307700e+000 9.804091e+001 3.616801e+003
ngli027 9.637354e-015 1.344193e+001 1.056506e+000 1.377720e+001 1.386295e+002 1.872296e+002
ngli028 8.068585e-014 1.654549e+001 1.233413e+000 1.804349e+001 1.548263e+002 1.743054e+003
ngli029 1.914500e-013 1.175127e+001 1.884981e+000 1.816171e+001 1.461660e+002 3.472298e+003
ngli030 9.421591e-015 8.774083e+000 1.112643e+000 1.854914e+001 1.666939e+002 2.639293e+003
5 0 ngli031 6.519850e-014 1.075179e+001 2.835638e+000 1.859460e+002 3.554844e+002 3.812733e+004
ngli032 9.158023e-014 7.234515e+000 4.350153e+000 6.183625e+001 2.095341e+002 2.905544e+004
ngli033 8.693897e-014 5.654870e+000 3.361718e+000 8.605783e+000 2.275203e+002 1.112341e+004
ngli034 4.095803e-014 7.666776e+000 2.297381e+000 8.870794e+001 2.479625e+002 1.266648e+004
ngli035 2.801555e-014 5.731701e+000 2.212312e+000 2.330378e+001 3.007367e+002 1.018107e+004
ngli036 9.489164e-014 7.197207e+000 3.442593e+000 1.334369e+002 1.664441e+002 3.118731e+004
ngli037 4.451216e-014 5.120758e+000 3.045119e+000 3.311893e+001 1.705582e+002 2.978091e+004
ngli038 1.209881e-013 1.040215e+001 2.232200e+000 3.160257e+001 1.850760e+002 9.883398e+004
ngli039 3.270165e-014 4.419012e+000 3.227204e+000 6.331038e+001 1.775115e+002 2.104416e+004
ngli040 3.839086e-014 4.911277e+000 4.354488e+000 2.532013e+001 9.500738e+001 5.440702e+004
1 ngli041 4.869972e-014 5.067345e+000 2.143286e+000 4.271932e+001 1.818259e+002 3.616780e+004
ngli042 3.528487e-014 7.558053e+000 2.007837e+000 5.303097e+001 2.194094e+002 2.291906e+004
ngli043 6.656050e-014 6.255945e+000 4.656806e+000 9.611899e+001 1.998361e+002 1.549316e+004
ngli044 5.521461e-014 4.147821e+000 4.274562e+000 9.867039e+000 1.798502e+002 2.529103e+004
ngli045 1.574175e-014 4.610036e+000 2.061798e+000 2.982776e+001 1.300914e+002 1.145401e+004
ngli046 4.733882e-014 3.748941e+000 3.624295e+000 5.847465e+001 2.125619e+002 4.004055e+004
ngli047 5.094250e-014 5.175540e+000 3.722850e+000 2.339170e+001 1.982951e+002 8.883461e+004
ngli048 1.052138e-013 3.646050e+000 3.666776e+000 2.164962e+001 1.365630e+002 9.178930e+004
ngli049 1.439086e-014 8.307761e+000 3.015854e+000 2.184738e+001 2.386089e+002 2.163121e+004
ngli050 3.757975e-014 7.882711e+000 2.269132e+000 5.641143e+001 1.646215e+002 6.128742e+003
2 ngli051 1.763566e-013 7.651040e+000 3.245241e+000 1.786667e+001 1.489225e+002 5.674561e+004
ngli052 4.280033e-014 4.521038e+000 2.883906e+000 3.618223e+001 1.052494e+002 4.982962e+004
ngli053 2.077444e-014 5.627178e+000 2.641736e+000 3.220198e+001 1.339164e+002 2.477893e+004
ngli054 2.361315e-014 4.627060e+000 2.363373e+000 4.688288e+001 1.403358e+002 5.466963e+004
ngli055 4.229254e-014 6.652549e+000 2.594482e+000 6.688743e+001 1.575106e+002 1.386699e+005
ngli056 4.163534e-014 3.528081e+000 5.433035e+000 2.041226e+001 1.031780e+002 1.376154e+005
ngli057 1.433238e-013 3.099626e+000 7.372160e+000 1.160231e+001 8.859513e+001 1.091632e+003
ngli058 3.857276e-014 4.160128e+000 2.802501e+000 4.176818e+001 1.333393e+002 8.095297e+003
ngli059 7.872107e-014 5.359616e+000 3.348420e+000 2.670423e+001 1.118561e+002 4.615694e+004
ngli060 2.819428e-014 2.724757e+000 5.432276e+000 4.669808e+001 1.658579e+002 5.434246e+004
10 0 ngli061 1.025234e-013 6.331090e+000 4.150622e+000 1.782780e+002 2.829718e+002 1.231334e+005
ngli062 1.045057e-013 8.098737e+000 4.223029e+000 2.966300e+002 2.923794e+002 3.486803e+005
ngli063 1.072592e-013 4.168465e+000 5.561640e+000 9.135877e+001 2.016044e+002 3.655372e+005
ngli064 1.399171e-013 8.717529e+000 2.399927e+000 1.781302e+002 2.432586e+002 2.555572e+005
ngli065 7.687097e-014 5.531735e+000 5.256498e+000 2.488956e+001 2.433618e+002 2.448978e+005
ngli066 9.169354e-014 6.827337e+000 3.437510e+000 1.958706e+002 3.063444e+002 4.407342e+005
ngli067 9.030385e-014 3.839023e+000 8.944292e+000 4.439361e+001 1.425485e+002 1.920335e+005
ngli068 5.780376e-014 5.217182e+000 7.344891e+000 2.212076e+002 2.627365e+002 1.136770e+005
ngli069 7.231581e-014 3.556506e+000 6.368829e+000 1.030165e+002 2.574188e+002 4.384150e+005
ngli070 1.376702e-013 5.978212e+000 4.539482e+000 1.164941e+002 3.071450e+002 1.329262e+005
1 ngli071 7.019597e-014 6.619845e+000 3.857133e+000 5.273874e+001 2.739734e+002 1.979007e+005
ngli072 1.339820e-013 3.710960e+000 5.152601e+000 4.318202e+001 1.611163e+002 9.632068e+004
ngli073 4.650989e-014 3.552949e+000 7.116371e+000 1.202777e+002 2.403273e+002 2.865258e+005
ngli074 5.283381e-014 4.776068e+000 6.087653e+000 1.688551e+002 1.635384e+002 3.639727e+005
ngli075 8.427037e-014 3.077958e+000 9.535127e+000 1.162328e+002 1.894017e+002 2.456102e+005
ngli076 5.005769e-014 3.376557e+000 7.114688e+000 1.906806e+002 2.135395e+002 1.185011e+005
ngli077 7.864710e-014 5.925089e+000 3.906998e+000 9.726994e+001 1.816221e+002 2.212767e+005
ngli078 3.986422e-014 3.085891e+000 6.788071e+000 1.504539e+002 2.489144e+002 4.280845e+005
ngli079 7.019045e-014 2.330327e+000 7.220824e+000 5.106830e+001 1.263676e+002 2.887425e+005
ngli080 2.604492e-013 3.708255e+000 7.617116e+000 9.357392e+001 1.679891e+002 4.220993e+005
2 ngli081 4.131102e-014 2.284663e+000 7.571656e+000 3.213760e+001 7.894637e+001 1.554558e+005
ngli082 5.756127e-014 3.826771e+000 5.518714e+000 6.879900e+001 1.615392e+002 3.840721e+005
ngli083 7.530010e-014 7.336746e+000 2.978701e+000 6.175716e+001 1.496934e+002 2.188266e+005
ngli084 1.347863e-013 2.870286e+000 7.922364e+000 5.399292e+001 1.339643e+002 2.344199e+005
ngli085 1.743702e-013 4.247034e+000 5.683751e+000 1.139846e+002 1.232876e+002 5.113863e+005
ngli086 8.555697e-014 9.156891e+000 2.272944e+000 5.178599e+001 1.243887e+002 2.373167e+005
ngli087 9.711381e-014 3.112701e+000 9.358531e+000 7.241497e+001 1.294714e+002 2.160288e+005
ngli088 7.497345e-014 2.571388e+000 7.975760e+000 5.803000e+001 1.920850e+002 4.681692e+004
ngli089 8.529945e-014 3.384263e+000 5.098512e+000 6.258488e+001 1.216629e+002 8.880706e+004
ngli090 5.457808e-014 6.087589e+000 2.748306e+000 1.772160e+001 6.871867e+001 2.060124e+005
20 0 ngli091 1.680351e-013 4.142555e+000 5.910655e+000 1.482996e+002 2.737201e+002 6.844871e+005
ngli092 1.683815e-013 4.011163e+000 6.756814e+000 5.885974e+002 4.078419e+002 6.297583e+005
ngli093 2.730507e-013 4.754539e+000 6.633682e+000 2.580665e+002 2.926442e+002 6.741491e+005
ngli094 1.398929e-013 4.469371e+000 5.627718e+000 3.323255e+002 2.632494e+002 4.979945e+005
ngli095 1.472098e-013 5.201803e+000 8.655270e+000 4.314956e+002 2.963939e+002 6.545308e+005
ngli096 1.141986e-013 4.816185e+000 5.409754e+000 2.470149e+002 2.449628e+002 5.760033e+005
ngli097 1.113140e-013 5.076867e+000 6.479525e+000 1.604164e+002 2.117693e+002 7.927265e+005
ngli098 5.062281e-013 5.966867e+000 4.436967e+000 2.984644e+002 2.719370e+002 6.142530e+005
ngli099 2.216220e-013 5.761774e+000 4.276531e+000 3.160636e+002 3.128526e+002 6.563409e+005
ngli100 1.169495e-013 4.817142e+000 6.732085e+000 3.935024e+002 3.507428e+002 7.916740e+005
1 ngli101 8.050856e-014 4.794128e+000 4.725886e+000 2.764555e+002 1.960555e+002 9.740355e+005
ngli102 8.509110e-014 3.617949e+000 5.950217e+000 1.717577e+002 1.463881e+002 4.515169e+005
ngli103 1.491339e-013 5.305134e+000 4.910277e+000 1.198038e+002 2.798719e+002 8.745743e+005
ngli104 1.237868e-013 4.467334e+000 6.211709e+000 2.762376e+002 2.284875e+002 6.766094e+005
ngli105 8.567274e-014 3.826253e+000 5.788021e+000 1.196420e+002 1.469071e+002 4.454145e+005
ngli106 1.178508e-013 4.294572e+000 5.477488e+000 1.626841e+002 1.563735e+002 6.996782e+005
ngli107 9.845077e-014 4.540158e+000 7.137431e+000 3.225108e+002 2.490500e+002 5.143042e+005
ngli108 1.358105e-013 4.273473e+000 6.743160e+000 3.012014e+002 1.994754e+002 5.888141e+005
ngli109 1.365241e-013 3.890004e+000 5.820417e+000 2.584417e+002 2.559387e+002 5.905666e+005
ngli110 2.132331e-013 3.340381e+000 5.222870e+000 1.679418e+002 1.828938e+002 7.240017e+005
2 ngli111 1.157593e-013 2.627845e+000 7.816847e+000 9.420923e+001 1.198240e+002 7.839103e+005
ngli112 1.668466e-013 2.477482e+000 8.522018e+000 1.348739e+002 1.330052e+002 6.622109e+005
ngli113 1.395779e-013 4.588548e+000 5.471741e+000 5.835584e+001 1.410771e+002 7.655933e+005
ngli114 3.122294e-013 2.463192e+000 1.135446e+001 1.868900e+002 1.207854e+002 7.109112e+005
ngli115 2.377652e-013 2.386440e+000 8.266196e+000 1.378337e+002 1.591674e+002 1.232511e+006
ngli116 8.455759e-014 3.245116e+000 8.819883e+000 1.642247e+002 1.476700e+002 9.157288e+005
ngli117 1.655490e-013 4.043256e+000 6.492305e+000 2.208851e+002 1.426182e+002 8.857105e+005
ngli118 1.811674e-013 3.556929e+000 7.886189e+000 1.454839e+002 1.412237e+002 9.241330e+005
ngli119 1.271550e-013 4.237087e+000 5.381771e+000 1.694161e+002 1.406184e+002 7.987707e+005
ngli120 2.100352e-013 4.485804e+000 5.598229e+000 1.710489e+002 1.517920e+002 7.175578e+005
50 0 ngli121 2.377552e-013 3.818769e+000 8.502132e+000 7.066345e+002 2.758892e+002 1.193459e+006
ngli122 3.417145e-013 3.425095e+000 8.123168e+000 6.559621e+002 2.315294e+002 1.145719e+006
ngli123 3.092067e-013 3.535264e+000 1.071719e+001 5.200207e+002 2.269356e+002 9.266195e+005
ngli124 2.242372e-013 4.095897e+000 7.786352e+000 6.809460e+002 2.411329e+002 1.210504e+006
ngli125 2.661426e-013 2.625041e+000 1.342364e+001 6.628288e+002 2.720969e+002 1.437667e+006
ngli126 3.661371e-013 3.642148e+000 9.428376e+000 8.854243e+002 2.720275e+002 1.080212e+006
ngli127 2.138163e-013 4.254233e+000 7.822792e+000 7.360534e+002 1.975744e+002 8.778927e+005
ngli128 2.064365e-013 3.433078e+000 7.386543e+000 7.215050e+002 2.351239e+002 1.085434e+006
ngli129 3.225056e-013 3.168273e+000 1.007778e+001 7.763457e+002 2.422041e+002 1.402011e+006
ngli130 3.603775e-013 3.754555e+000 8.428799e+000 5.930559e+002 3.132761e+002 1.505922e+006
1 ngli131 1.826339e-013 2.922941e+000 1.042594e+001 5.372723e+002 1.746546e+002 9.793476e+005
ngli132 2.632967e-013 2.508600e+000 1.037128e+001 5.098613e+002 1.764072e+002 1.589892e+006
ngli133 2.754585e-013 2.647346e+000 9.644679e+000 5.022307e+002 2.026476e+002 9.377800e+005
ngli134 1.943098e-013 3.793733e+000 1.011637e+001 6.452488e+002 1.840392e+002 1.189903e+006
ngli135 2.273230e-013 3.937031e+000 7.286493e+000 5.302858e+002 1.965154e+002 1.398215e+006
ngli136 4.131649e-013 3.248612e+000 9.216598e+000 4.290573e+002 2.164655e+002 1.410622e+006
ngli137 2.611180e-013 2.917157e+000 1.185133e+001 6.381232e+002 1.851718e+002 1.426825e+006
ngli138 2.569237e-013 3.189020e+000 1.182078e+001 5.026205e+002 1.690641e+002 1.252462e+006
ngli139 2.282499e-013 2.805813e+000 1.095895e+001 4.453389e+002 1.820842e+002 1.202585e+006
ngli140 4.129086e-013 4.771345e+000 6.108109e+000 3.834983e+002 1.897409e+002 1.345995e+006
2 ngli141 2.251684e-013 3.889066e+000 5.475651e+000 4.191136e+002 1.441538e+002 1.441323e+006
ngli142 2.614264e-013 1.990963e+000 1.217799e+001 3.351742e+002 1.444319e+002 1.343614e+006
ngli143 2.036280e-013 2.792700e+000 6.690209e+000 3.130869e+002 1.235855e+002 1.167639e+006
ngli144 2.103063e-013 4.254349e+000 7.177671e+000 3.650102e+002 1.335965e+002 1.131814e+006
ngli145 1.529319e-013 3.529130e+000 5.817891e+000 2.986061e+002 1.243203e+002 9.174321e+005
ngli146 1.888333e-013 3.614745e+000 7.334339e+000 3.333603e+002 1.239359e+002 1.181022e+006
ngli147 1.628923e-013 2.541782e+000 9.128928e+000 4.248212e+002 1.380700e+002 8.379257e+005
ngli148 2.059183e-013 2.850869e+000 9.380913e+000 3.673815e+002 1.433797e+002 1.291643e+006
ngli149 3.212752e-013 3.929813e+000 7.439027e+000 3.610974e+002 1.527770e+002 1.498377e+006
ngli150 3.798925e-013 4.003550e+000 6.263863e+000 2.676511e+002 1.272888e+002 1.280738e+006
100 0 ngli151 5.099932e-013 3.535230e+000 8.502964e+000 1.230104e+003 2.602532e+002 1.625554e+006
ngli152 5.161120e-013 3.672496e+000 1.073084e+001 1.513048e+003 2.629966e+002 1.516621e+006
ngli153 6.840372e-013 2.551412e+000 1.250278e+001 1.438728e+003 2.642613e+002 1.301931e+006
ngli154 5.622310e-013 3.721014e+000 8.822210e+000 1.537428e+003 2.680751e+002 1.453243e+006
ngli155 6.551065e-013 2.903789e+000 9.923164e+000 1.273890e+003 2.555331e+002 1.522494e+006
ngli156 6.071525e-013 4.034346e+000 9.356552e+000 1.315077e+003 2.784895e+002 1.488711e+006
ngli157 4.767152e-013 2.778385e+000 1.274227e+001 1.396433e+003 2.435415e+002 1.339022e+006
ngli158 5.634910e-013 3.673531e+000 8.992027e+000 1.239708e+003 2.653872e+002 1.447174e+006
ngli159 4.812508e-013 3.185642e+000 9.989112e+000 1.443636e+003 2.474071e+002 1.242850e+006
ngli160 5.121946e-013 3.569665e+000 8.927811e+000 1.455431e+003 2.537128e+002 1.458350e+006
1 ngli161 5.540519e-013 2.730049e+000 9.515086e+000 1.178532e+003 1.950160e+002 1.511202e+006
ngli162 4.561855e-013 2.497635e+000 1.313991e+001 9.644088e+002 2.248833e+002 1.960367e+006
ngli163 4.946803e-013 3.612248e+000 9.645764e+000 1.248980e+003 2.062723e+002 1.682096e+006
ngli164 4.168754e-013 2.474883e+000 1.486750e+001 1.109151e+003 2.087505e+002 1.536730e+006
ngli165 3.953781e-013 2.825769e+000 1.138775e+001 9.043206e+002 1.842925e+002 1.380859e+006
ngli166 3.631998e-013 3.046888e+000 1.051906e+001 1.104221e+003 2.171855e+002 1.552579e+006
ngli167 3.882550e-013 2.853879e+000 1.084932e+001 1.286025e+003 2.090721e+002 1.549360e+006
ngli168 4.426446e-013 3.856764e+000 8.662715e+000 8.878569e+002 1.879970e+002 1.397375e+006
ngli169 5.509485e-013 3.478352e+000 7.817472e+000 8.813455e+002 1.795586e+002 1.172419e+006
ngli170 4.209064e-013 3.846385e+000 7.283081e+000 1.224515e+003 2.108425e+002 1.268950e+006
2 ngli171 4.590453e-013 2.895476e+000 9.095571e+000 8.606230e+002 1.425211e+002 1.499959e+006
ngli172 3.324585e-013 2.808933e+000 8.973381e+000 5.934902e+002 1.253297e+002 1.689187e+006
ngli173 3.203302e-013 2.890144e+000 9.605809e+000 7.368184e+002 1.482064e+002 1.488044e+006
ngli174 4.763941e-013 3.022922e+000 7.675201e+000 5.962645e+002 1.280670e+002 1.452443e+006
ngli175 3.877642e-013 2.665426e+000 1.148351e+001 7.791374e+002 1.427484e+002 1.653917e+006
ngli176 3.469764e-013 2.940694e+000 1.005259e+001 9.437013e+002 1.636546e+002 1.762167e+006
ngli177 4.617687e-013 2.829030e+000 1.103559e+001 6.119093e+002 1.247778e+002 1.414485e+006
ngli178 4.268612e-013 2.783690e+000 1.113068e+001 7.595984e+002 1.463604e+002 1.760992e+006
ngli179 4.223974e-013 3.239993e+000 8.999931e+000 6.766347e+002 1.612297e+002 1.772516e+006
ngli180 4.200757e-013 3.044116e+000 8.398336e+000 6.241160e+002 1.327712e+002 1.521299e+006
200 0 ngli181 9.394201e-013 3.261032e+000 1.103256e+001 2.857126e+003 2.684384e+002 1.627728e+006
ngli182 9.638039e-013 2.559718e+000 1.322313e+001 3.070178e+003 2.425944e+002 1.573291e+006
ngli183 9.992164e-013 3.587998e+000 9.491217e+000 3.179522e+003 2.394251e+002 1.555872e+006
ngli184 8.629842e-013 3.241379e+000 9.612838e+000 2.911955e+003 2.470514e+002 1.607368e+006
ngli185 9.857276e-013 2.264528e+000 1.493241e+001 2.335421e+003 2.360429e+002 1.404789e+006
ngli186 9.195530e-013 3.518364e+000 1.154588e+001 3.150401e+003 2.482769e+002 1.413264e+006
ngli187 1.035830e-012 2.748423e+000 1.182483e+001 2.991528e+003 2.546148e+002 1.483933e+006
ngli188 1.358693e-012 3.418486e+000 1.191884e+001 2.506190e+003 2.320990e+002 1.602762e+006
ngli189 9.436818e-013 3.556460e+000 1.197231e+001 2.807065e+003 2.621653e+002 1.724674e+006
ngli190 8.080606e-013 3.039520e+000 1.048057e+001 3.425480e+003 2.452609e+002 1.596886e+006
1 ngli191 7.676766e-013 2.467357e+000 1.617246e+001 1.767580e+003 1.740935e+002 1.591741e+006
ngli192 9.144826e-013 3.294471e+000 1.110710e+001 2.030836e+003 1.713097e+002 1.482164e+006
ngli193 8.214132e-013 3.446287e+000 9.992696e+000 2.144006e+003 1.894443e+002 1.568532e+006
ngli194 8.863865e-013 1.947933e+000 2.104194e+001 2.318641e+003 2.055600e+002 1.754945e+006
ngli195 8.889315e-013 2.704806e+000 1.230871e+001 2.259361e+003 2.165207e+002 1.877328e+006
ngli196 8.358887e-013 3.409176e+000 1.199653e+001 1.880983e+003 2.022817e+002 1.781740e+006
ngli197 8.329204e-013 2.659134e+000 1.265950e+001 1.961027e+003 1.990760e+002 1.719953e+006
ngli198 8.188281e-013 3.287930e+000 8.729633e+000 2.025042e+003 2.043494e+002 1.559160e+006
ngli199 9.564053e-013 3.492018e+000 1.066074e+001 2.084228e+003 2.059878e+002 1.545379e+006
ngli200 6.863145e-013 2.482557e+000 1.388457e+001 1.719504e+003 1.882940e+002 1.588248e+006
2 ngli201 8.284302e-013 2.453698e+000 1.184336e+001 1.305226e+003 1.254329e+002 1.679977e+006
ngli202 7.315483e-013 2.962598e+000 1.015362e+001 1.520515e+003 1.429879e+002 1.713261e+006
ngli203 9.933056e-013 2.630719e+000 1.051477e+001 1.335004e+003 1.271924e+002 1.698670e+006
ngli204 8.897212e-013 3.505187e+000 7.167695e+000 1.475784e+003 1.355787e+002 1.955065e+006
ngli205 8.771972e-013 2.958135e+000 1.241684e+001 1.363949e+003 1.361676e+002 1.684702e+006
ngli206 7.244975e-013 2.323030e+000 1.476122e+001 1.531877e+003 1.438329e+002 1.975879e+006
ngli207 7.656349e-013 3.028900e+000 8.610300e+000 1.473441e+003 1.340064e+002 1.772089e+006
ngli208 7.435889e-013 2.659501e+000 1.090793e+001 1.617992e+003 1.392737e+002 1.972698e+006
ngli209 7.171260e-013 2.364948e+000 1.140705e+001 1.110753e+003 1.316528e+002 1.564968e+006
ngli210 7.607409e-013 2.782036e+000 9.740595e+000 1.348196e+003 1.323076e+002 1.765857e+006
500 0 ngli211 2.279294e-012 2.868122e+000 1.239188e+001 6.248843e+003 2.373356e+002 1.687722e+006
ngli212 2.502999e-012 2.995281e+000 1.141989e+001 7.422840e+003 2.572857e+002 1.712340e+006
ngli213 2.237310e-012 3.005032e+000 1.361323e+001 6.609158e+003 2.485580e+002 1.847384e+006
ngli214 2.693580e-012 3.003527e+000 1.348934e+001 6.742283e+003 2.523410e+002 1.774159e+006
ngli215 2.495561e-012 2.554339e+000 1.419431e+001 6.602380e+003 2.560626e+002 1.673822e+006
ngli216 2.598489e-012 2.897368e+000 1.438696e+001 6.453041e+003 2.415362e+002 1.625512e+006
ngli217 2.739913e-012 2.785442e+000 1.445815e+001 6.862980e+003 2.539011e+002 1.753191e+006
ngli218 2.480855e-012 2.368960e+000 1.683667e+001 6.604528e+003 2.548647e+002 1.614935e+006
ngli219 2.330114e-012 2.338605e+000 1.379769e+001 6.473400e+003 2.365023e+002 1.650046e+006
ngli220 2.350548e-012 3.272097e+000 1.146752e+001 6.543879e+003 2.582822e+002 1.734723e+006
1 ngli221 2.171299e-012 2.393613e+000 1.633310e+001 5.187700e+003 1.936025e+002 1.798997e+006
ngli222 2.115177e-012 2.580922e+000 1.244299e+001 5.212933e+003 1.974684e+002 1.709696e+006
ngli223 1.782422e-012 2.301333e+000 1.674028e+001 4.830314e+003 1.809640e+002 1.643423e+006
ngli224 2.025777e-012 2.240758e+000 1.626479e+001 5.070558e+003 1.847993e+002 1.771702e+006
ngli225 1.858743e-012 2.541182e+000 1.347168e+001 4.751979e+003 1.854403e+002 1.663254e+006
ngli226 2.059192e-012 3.024200e+000 1.023890e+001 4.845396e+003 1.962650e+002 1.728716e+006
ngli227 2.187779e-012 2.493699e+000 1.457597e+001 5.098051e+003 1.896889e+002 1.749191e+006
ngli228 2.035854e-012 2.814586e+000 1.368346e+001 4.996832e+003 1.881747e+002 1.846783e+006
ngli229 2.020799e-012 2.938072e+000 1.219616e+001 5.488533e+003 1.972761e+002 1.775394e+006
ngli230 1.970576e-012 2.223950e+000 1.583999e+001 4.919547e+003 1.997170e+002 1.729174e+006
2 ngli231 1.798762e-012 2.129699e+000 1.465598e+001 3.314991e+003 1.290424e+002 1.794611e+006
ngli232 2.048831e-012 2.273860e+000 1.340514e+001 3.796829e+003 1.398331e+002 1.909787e+006
ngli233 1.875859e-012 2.374179e+000 1.523291e+001 3.596819e+003 1.347904e+002 1.765675e+006
ngli234 1.970038e-012 2.215855e+000 1.483958e+001 3.909260e+003 1.434827e+002 2.035400e+006
ngli235 1.791983e-012 2.476524e+000 1.346211e+001 3.524587e+003 1.387531e+002 1.901378e+006
ngli236 1.616190e-012 2.464447e+000 1.203878e+001 3.304382e+003 1.303710e+002 1.754229e+006
ngli237 1.964685e-012 2.103361e+000 1.503955e+001 3.567914e+003 1.337994e+002 1.951906e+006
ngli238 1.729279e-012 2.136823e+000 1.370323e+001 3.547639e+003 1.398660e+002 2.077871e+006
ngli239 2.092837e-012 2.285129e+000 1.493442e+001 3.502230e+003 1.435336e+002 1.962432e+006
ngli240 2.185991e-012 2.638867e+000 1.374475e+001 3.596072e+003 1.436601e+002 1.926077e+006
1000 0 ngli241 4.686582e-012 2.925833e+000 1.416772e+001 1.350673e+004 2.568115e+002 1.699023e+006
ngli242 4.985797e-012 2.590800e+000 1.587504e+001 1.407889e+004 2.522623e+002 1.721253e+006
ngli243 5.073720e-012 2.693971e+000 1.470555e+001 1.365259e+004 2.422863e+002 1.723434e+006
ngli244 4.514671e-012 2.992802e+000 1.245743e+001 1.302476e+004 2.527114e+002 1.717103e+006
ngli245 5.373627e-012 2.812001e+000 1.527970e+001 1.429903e+004 2.558611e+002 1.744724e+006
ngli246 4.620086e-012 2.469518e+000 1.607100e+001 1.353309e+004 2.429092e+002 1.745424e+006
ngli247 4.471504e-012 2.436328e+000 1.512140e+001 1.294255e+004 2.581676e+002 1.821038e+006
ngli248 4.707864e-012 2.881960e+000 1.525768e+001 1.241700e+004 2.449560e+002 1.736758e+006
ngli249 4.825871e-012 2.747080e+000 1.428515e+001 1.323158e+004 2.529062e+002 1.700347e+006
ngli250 5.061058e-012 2.786780e+000 1.668064e+001 1.383051e+004 2.527167e+002 1.766449e+006
1 ngli251 4.140633e-012 2.452008e+000 1.630560e+001 1.012912e+004 1.922659e+002 1.851078e+006
ngli252 4.061470e-012 2.307552e+000 1.657971e+001 9.717077e+003 1.843847e+002 1.739225e+006
ngli253 3.617594e-012 2.662331e+000 1.391868e+001 1.145309e+004 1.910236e+002 1.750100e+006
ngli254 3.766863e-012 2.755903e+000 1.537406e+001 1.049153e+004 1.994247e+002 1.815396e+006
ngli255 3.573380e-012 2.717985e+000 1.278800e+001 9.932979e+003 1.941997e+002 1.765252e+006
ngli256 4.019866e-012 2.066688e+000 2.165118e+001 1.125307e+004 1.952241e+002 1.833226e+006
ngli257 4.012667e-012 2.249093e+000 1.765254e+001 1.054188e+004 1.958046e+002 1.793155e+006
ngli258 3.892123e-012 2.081737e+000 1.891458e+001 1.020698e+004 1.921022e+002 1.829711e+006
ngli259 4.108216e-012 2.035827e+000 1.789251e+001 1.019445e+004 2.012459e+002 1.872343e+006
ngli260 4.151630e-012 1.716982e+000 1.941843e+001 1.106506e+004 1.968632e+002 1.855335e+006
2 ngli261 3.842171e-012 2.372508e+000 1.296612e+001 7.006573e+003 1.379814e+002 1.875214e+006
ngli262 3.616686e-012 2.158715e+000 1.552257e+001 6.757078e+003 1.330429e+002 1.862343e+006
ngli263 3.723303e-012 1.913259e+000 1.808274e+001 6.783114e+003 1.394016e+002 1.861158e+006
ngli264 3.535714e-012 2.121942e+000 1.465147e+001 7.135992e+003 1.375468e+002 1.861956e+006
ngli265 3.713599e-012 1.935552e+000 1.751539e+001 6.894539e+003 1.334644e+002 1.919407e+006
ngli266 3.613757e-012 2.302811e+000 1.582951e+001 6.723314e+003 1.408887e+002 1.868483e+006
ngli267 3.720617e-012 2.745901e+000 1.241230e+001 6.870741e+003 1.348954e+002 1.925180e+006
ngli268 3.580037e-012 2.295438e+000 1.344243e+001 7.278651e+003 1.387908e+002 1.933619e+006
ngli269 3.807373e-012 1.902336e+000 1.704662e+001 7.060199e+003 1.402687e+002 1.957994e+006
ngli270 3.615451e-012 2.356020e+000 1.421773e+001 6.725194e+003 1.336185e+002 1.863658e+006
2000 0 ngli271 9.748027e-012 2.577514e+000 1.645231e+001 2.652705e+004 2.499767e+002 1.655607e+006
ngli272 1.006870e-011 2.936336e+000 1.365845e+001 2.829512e+004 2.505045e+002 1.710218e+006
ngli273 1.006175e-011 2.362453e+000 1.882393e+001 2.607136e+004 2.498994e+002 1.708543e+006
ngli274 9.637284e-012 2.439025e+000 1.939828e+001 2.749580e+004 2.483859e+002 1.702712e+006
ngli275 9.581746e-012 2.816846e+000 1.471551e+001 2.737409e+004 2.546322e+002 1.755990e+006
ngli276 9.860487e-012 2.736216e+000 1.554916e+001 2.746745e+004 2.495941e+002 1.804650e+006
ngli277 9.664569e-012 2.808118e+000 1.414390e+001 2.705383e+004 2.513543e+002 1.743624e+006
ngli278 9.507153e-012 2.564795e+000 1.713729e+001 2.726563e+004 2.459188e+002 1.756687e+006
ngli279 9.657589e-012 2.266239e+000 1.864422e+001 2.787961e+004 2.582492e+002 1.768649e+006
ngli280 9.365205e-012 2.355924e+000 1.866669e+001 2.892256e+004 2.618746e+002 1.858592e+006
1 ngli281 7.866721e-012 2.600116e+000 1.565916e+001 2.119760e+004 1.897178e+002 1.760052e+006
ngli282 7.909579e-012 2.336686e+000 1.882867e+001 1.951563e+004 1.946665e+002 1.736830e+006
ngli283 7.944236e-012 2.124958e+000 1.739241e+001 2.011591e+004 1.961906e+002 1.835669e+006
ngli284 7.679440e-012 2.727824e+000 1.544726e+001 2.045200e+004 1.956345e+002 1.775399e+006
ngli285 7.856646e-012 2.388475e+000 1.753354e+001 2.159712e+004 1.915892e+002 1.776365e+006
ngli286 7.584611e-012 2.169323e+000 2.055241e+001 1.989196e+004 1.905994e+002 1.825500e+006
ngli287 7.894750e-012 2.142291e+000 1.787126e+001 2.075014e+004 1.911276e+002 1.827636e+006
ngli288 8.199392e-012 2.087960e+000 1.807975e+001 2.201505e+004 1.973880e+002 1.882520e+006
ngli289 7.408393e-012 2.497545e+000 1.863378e+001 1.976896e+004 1.906253e+002 1.836103e+006
ngli290 7.896568e-012 1.909965e+000 1.900160e+001 2.138289e+004 1.949496e+002 1.801512e+006
2 ngli291 7.750413e-012 2.229517e+000 1.435130e+001 1.428147e+004 1.390719e+002 1.925713e+006
ngli292 7.324867e-012 2.039330e+000 1.797503e+001 1.349261e+004 1.358616e+002 1.887514e+006
ngli293 7.350495e-012 2.050410e+000 1.709840e+001 1.398355e+004 1.371427e+002 1.898997e+006
ngli294 7.117722e-012 2.029544e+000 1.796838e+001 1.433866e+004 1.386198e+002 1.910123e+006
ngli295 6.990016e-012 2.371813e+000 1.463055e+001 1.457408e+004 1.365691e+002 1.908886e+006
ngli296 7.286976e-012 2.275541e+000 1.581930e+001 1.422488e+004 1.382224e+002 1.881024e+006
ngli297 7.392648e-012 2.505221e+000 1.638898e+001 1.389834e+004 1.355639e+002 1.929770e+006
ngli298 7.322883e-012 1.930623e+000 1.697094e+001 1.410663e+004 1.366024e+002 1.898510e+006
ngli299 7.559138e-012 1.937703e+000 1.929160e+001 1.420015e+004 1.347446e+002 1.885250e+006
ngli300 6.926560e-012 1.922170e+000 1.977936e+001 1.432638e+004 1.352487e+002 1.901982e+006
Some Computational Results:
Multistart (MATLAB/fminunc) BARON version 9.0.2 under GAMS Distribution 23.3
Dimension Difficulty Level Problem-ID Number of Successful Trials out of 10,000 Trials Number of Iterations CPU Time in Seconds (Intel Core2Duo E6700)
2 0 ngli001 4713 7 0.359
ngli002 4690 11 0.391
ngli003 5330 9 0.360
ngli004 6400 3 0.454
ngli005 4522 15 0.359
ngli006 3819 9 0.469
ngli007 4551 7 0.469
ngli008 4516 17 0.359
ngli009 4080 9 0.360
ngli010 4709 9 0.453
1 ngli011 3958 15 0.344
ngli012 4350 19 0.375
ngli013 3822 11 0.454
ngli014 3422 17 0.453
ngli015 3886 9 0.469
ngli016 3320 7 0.360
ngli017 3108 27 0.469
ngli018 4314 19 0.484
ngli019 3857 15 0.469
ngli020 3110 19 0.454
2 ngli021 3007 19 0.469
ngli022 2977 25 0.454
ngli023 2928 21 0.454
ngli024 3416 11 0.469
ngli025 2794 35 0.453
ngli026 3104 23 0.468
ngli027 3432 21 0.454
ngli028 3381 13 0.453
ngli029 3282 27 0.454
ngli030 3569 11 0.453
5 0 ngli031 1745 73 0.672
ngli032 1330 209 0.906
ngli033 1324 293 1.109
ngli034 1454 125 0.797
ngli035 2155 185 1.001
ngli036 1542 93 0.672
ngli037 1327 223 0.797
ngli038 726 225 0.891
ngli039 870 101 0.734
ngli040 1208 93 0.719
1 ngli041 657 295 1.250
ngli042 632 569 1.844
ngli043 651 281 1.313
ngli044 884 235 0.953
ngli045 703 527 1.500
ngli046 507 389 1.250
ngli047 716 335 1.438
ngli048 413 709 2.094
ngli049 1215 393 1.438
ngli050 584 443 1.547
2 ngli051 765 937 2.547
ngli052 582 655 1.969
ngli053 564 877 2.953
ngli054 419 584 1.891
ngli055 551 697 2.204
ngli056 478 1063 2.938
ngli057 509 609 2.141
ngli058 723 697 2.094
ngli059 611 775 2.266
ngli060 474 1363 3.344
10 0 ngli061 170 15937 72.381
ngli062 168 7843 39.004
ngli063 49 24947 117.495
ngli064 114 10389 47.317
ngli065 111 21441 85.914
ngli066 150 8839 42.019
ngli067 95 9949 42.972
ngli068 196 6491 30.894
ngli069 91 14339 68.772
ngli070 98 12263 58.755
1 ngli071 43 60035 274.806
ngli072 45 44987 194.861
ngli073 76 80543 378.503
ngli074 29 49255 208.785
ngli075 35 35729 157.904
ngli076 43 16037 75.397
ngli077 123 50741 236.006
ngli078 73 39829 184.266
ngli079 39 59933 264.039
ngli080 10 161589 661.715
2 ngli081 11 81347 339.327
ngli082 16 84107 344.754
ngli083 27 116070 492.51
ngli084 10 332699 1407.792
ngli085 8 261757 1047.547
ngli086 3 294828 1155.353
ngli087 11 143377 562.473
ngli088 13 164741 739.176
ngli089 15 260004 1074.19
ngli090 2 410948 1764.638
20 0 ngli091 0
ngli092 1
ngli093 0
ngli094 1
ngli095 2
ngli096 1
ngli097 3
ngli098 0
ngli099 0
ngli100 1
1 ngli101 1
ngli102 0
ngli103 0
ngli104 0
ngli105 0
ngli106 0
ngli107 0
ngli108 0
ngli109 2
ngli110 1
2 ngli111 0
ngli112 0
ngli113 0
ngli114 0
ngli115 0
ngli116 0
ngli117 0
ngli118 0
ngli119 0
ngli120 0
50 0 ngli121 0
ngli122 0
ngli123 0
ngli124 0
ngli125 0
ngli126 0
ngli127 0
ngli128 0
ngli129 0
ngli130 0
1 ngli131 0
ngli132 0
ngli133 0
ngli134 0
ngli135 0
ngli136 0
ngli137 0
ngli138 0
ngli139 0
ngli140 0
2 ngli141 0
ngli142 0
ngli143 0
ngli144 0
ngli145 0
ngli146 0
ngli147 0
ngli148 0
ngli149 0
ngli150 0
100 0 ngli151 0
ngli152 0
ngli153 0
ngli154 0
ngli155 0
ngli156 0
ngli157 0
ngli158 0
ngli159 0
ngli160 0
1 ngli161 0
ngli162 0
ngli163 0
ngli164 0
ngli165 0
ngli166 0
ngli167 0
ngli168 0
ngli169 0
ngli170 0
2 ngli171 0
ngli172 0
ngli173 0
ngli174 0
ngli175 0
ngli176 0
ngli177 0
ngli178 0
ngli179 0
ngli180 0
200 0 ngli181 0
ngli182 0
ngli183 0
ngli184 0
ngli185 0
ngli186 0
ngli187 0
ngli188 0
ngli189 0
ngli190 0
1 ngli191 0
ngli192 0
ngli193 0
ngli194 0
ngli195 0
ngli196 0
ngli197 0
ngli198 0
ngli199 0
ngli200 0
2 ngli201 0
ngli202 0
ngli203 0
ngli204 0
ngli205 0
ngli206 0
ngli207 0
ngli208 0
ngli209 0
ngli210 0
500 0 ngli211 0
ngli212 0
ngli213 0
ngli214 0
ngli215 0
ngli216 0
ngli217 0
ngli218 0
ngli219 0
ngli220 0
1 ngli221 0
ngli222 0
ngli223 0
ngli224 0
ngli225 0
ngli226 0
ngli227 0
ngli228 0
ngli229 0
ngli230 0
2 ngli231 0
ngli232 0
ngli233 0
ngli234 0
ngli235 0
ngli236 0
ngli237 0
ngli238 0
ngli239 0
ngli240 0
1000 0 ngli241 0
ngli242 0
ngli243 0
ngli244 0
ngli245 0
ngli246 0
ngli247 0
ngli248 0
ngli249 0
ngli250 0
1 ngli251 0
ngli252 0
ngli253 0
ngli254 0
ngli255 0
ngli256 0
ngli257 0
ngli258 0
ngli259 0
ngli260 0
2 ngli261 0
ngli262 0
ngli263 0
ngli264 0
ngli265 0
ngli266 0
ngli267 0
ngli268 0
ngli269 0
ngli270 0
2000 0 ngli271 0
ngli272 0
ngli273 0
ngli274 0
ngli275 0
ngli276 0
ngli277 0
ngli278 0
ngli279 0
ngli280 0
1 ngli281 0
ngli282 0
ngli283 0
ngli284 0
ngli285 0
ngli286 0
ngli287 0
ngli288 0
ngli289 0
ngli290 0
2 ngli291 0
ngli292 0
ngli293 0
ngli294 0
ngli295 0
ngli296 0
ngli297 0
ngli298 0
ngli299 0
ngli300 0
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