Steve Jacobsen (jacobsen@ee.ucla.edu), K. Moshirvaziri (moshir@ee.ucla.edu) CONCAVE MININIMIZATION PROBLEM (m=25, n=18): min f(x) Ax < b x > 0 where f(x) = xQx + rx + s A,b= -1 -10 -6 10 8 -1 5 -8 4 4 8 -1 1 8 -7 -5 5 -6 14 2 4 -10 -10 -6 -4 3 -1 -9 6 6 -4 -0 -4 1 -6 3 0 -23 -1 -3 -2 10 4 6 -2 2 9 7 10 -3 7 6 7 6 -1 9 76 1 -7 1 2 -10 -4 -9 -7 7 2 -5 -10 9 6 8 5 -10 10 -5 -1 1 7 7 -10 -4 6 -0 4 10 9 -3 -1 2 -8 7 3 9 42 -4 -6 -9 -2 -0 -2 -8 1 -6 8 1 -4 -2 9 3 2 -2 4 -10 -1 -9 5 -4 -7 -2 -3 2 -6 6 -5 -5 -5 1 2 6 8 8 -4 2 4 1 -4 6 -2 -7 3 10 5 4 10 -2 4 7 8 -3 -8 44 5 4 -0 -2 6 3 -8 -8 10 3 3 -8 6 1 -4 -5 -5 4 11 2 5 7 -5 -5 5 -3 -5 -4 -2 2 -0 -6 -4 -1 7 -2 -7 -10 4 5 7 9 3 -9 2 8 -10 6 5 -6 4 3 -9 -6 -6 -1 13 -9 3 -6 -0 1 -10 3 6 5 2 5 -4 3 6 -6 -10 2 3 -0 -5 -0 -1 -8 -7 -5 1 -0 -8 -1 -2 -1 4 -4 -2 1 1 10 -23 9 -0 4 -4 3 9 3 3 -4 -3 -7 3 -9 8 8 -5 -4 -4 14 1 -9 -4 3 -3 2 -8 5 0 -2 8 -2 -4 3 -2 -5 2 9 -0 -6 -4 4 7 -5 4 -9 1 4 -8 5 4 -7 -8 -5 -7 5 -9 -27 5 -9 -1 -10 3 -4 9 -8 -8 10 -7 -4 5 -2 -5 10 9 5 1 6 -0 -5 -3 2 9 2 6 -1 -2 6 -2 -3 -5 1 4 -5 -1 13 -5 9 1 8 1 2 2 -1 -7 -4 -4 6 7 -7 1 -3 -4 2 8 3 3 -2 6 -1 -8 -4 3 2 -4 4 7 -6 4 -6 -0 8 9 24 -3 -0 6 -6 0 -2 -9 6 9 2 -1 -6 7 -8 5 -3 5 5 11 -6 1 9 -8 5 5 -0 8 6 8 -2 -6 -9 1 -8 10 4 -3 19 -3 6 -5 -1 5 -4 6 -6 -5 7 9 4 5 8 8 4 -5 -3 34 1 -4 3 -5 1 2 -2 -0 10 -5 -4 -1 -10 3 -8 0 -5 -7 -27 9 7 9 6 5 5 6 8 4 3 2 1 6 1 5 10 7 4 1020 r= -2.114132494707088e+02 8.238010557313024e+02 -8.369415706426598e+02 2.309655871391150e+03 3.007532181312794e+03 7.432082591793991e+02 1.440711645994997e+03 9.452061288353003e+02 1.748175814137002e+03 3.392635555639058e+02 1.250701450785499e+03 9.832296147554232e+02 1.303523545723276e+03 1.947855086698289e+03 5.264634581671090e+02 5.572793671994666e+02 -1.102929651646569e+03 5.388044299036114e+02 s= -1.280460412722986e+04 Q= -205 52 15 163 -20 -15 -109 28 93 -49 114 30 108 -140 -14 -54 -8 -33 52 -403 85 -73 -101 -27 -90 -28 109 139 -157 -227 11 58 -8 161 140 186 15 85 -278 -14 61 -131 178 -57 -97 129 160 21 105 90 -7 -33 -18 45 163 -73 -14 -547 -53 -91 166 -88 -269 219 -162 -188 -48 -68 10 68 130 -59 -20 -101 61 -53 -297 -62 -217 -41 8 -36 -49 -143 -64 -88 -14 -0 15 59 -15 -27 -131 -91 -62 -299 12 -64 -38 119 13 -59 115 8 -77 66 118 195 -109 -90 178 166 -217 12 -420 111 331 -159 38 -98 -24 -99 33 -69 8 92 28 -28 -57 -88 -41 -64 111 -240 -139 119 -25 -58 116 49 12 181 -100 -11 93 109 -97 -269 8 -38 331 -139 -518 102 -109 97 -125 -39 -76 35 68 -135 -49 139 129 219 -36 119 -159 119 102 -388 -34 212 -227 -116 -137 -243 -64 -224 114 -157 160 -162 -49 13 38 -25 -109 -34 -427 -94 -17 -35 -17 36 -2 70 30 -227 21 -188 -143 -59 -98 -58 97 212 -94 -328 183 1 125 141 -5 202 108 11 105 -48 -64 115 -24 116 -125 -227 -17 183 -505 -0 -173 -137 145 -259 -140 58 90 -68 -88 8 -99 49 -39 -116 -35 1 -0 -431 -199 -141 172 -138 -14 -8 -7 10 -14 -77 33 12 -76 -137 -17 125 -173 -199 -359 -40 235 -103 -54 161 -33 68 -0 66 -69 181 35 -243 36 141 -137 -141 -40 -390 -12 -203 -8 140 -18 130 15 118 8 -100 68 -64 -2 -5 145 172 235 -12 -430 -89 -33 186 45 -59 59 195 92 -11 -135 -224 70 202 -259 -138 -103 -203 -89 -536 best found x= 2.587859095761357E+00 1.614275095869258E+00 1.031627717284751E+00 2.837215406057890E+00 0.000000000000000E+00 0.000000000000000E+00 2.296944404774393E+00 0.000000000000000E+00 1.479625311186441E+00 0.000000000000000E+00 9.287888880685808E-01 8.082722474085888E-02 8.357643034120608E-01 0.000000000000000E+00 3.988035839204950E+00 1.500421888372609E+00 3.415492768787272E+00 0.000000000000000E+00