Steve Jacobsen (jacobsen@ee.ucla.edu), K. Moshirvaziri (moshir@ee.ucla.edu) CONCAVE MININIMIZATION PROBLEM (m=25, n=20): 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 8 -0 17 2 4 -10 -10 -6 -4 3 -1 -9 6 6 -4 -0 -4 1 -6 3 0 3 6 -17 -1 -3 -2 10 4 6 -2 2 9 7 10 -3 7 6 7 6 -1 9 7 5 85 1 -7 1 2 -10 -4 -9 -7 7 2 -5 -10 9 6 8 5 -10 10 2 -8 -15 -1 1 7 7 -10 -4 6 -0 4 10 9 -3 -1 2 -8 7 3 9 0 -8 30 -4 -6 -9 -2 -0 -2 -8 1 -6 8 1 -4 -2 9 3 2 -2 4 0 2 -11 -1 -9 5 -4 -7 -2 -3 2 -6 6 -5 -5 -5 1 2 6 8 8 1 -7 -13 2 4 1 -4 6 -2 -7 3 10 5 4 10 -2 4 7 8 -3 -8 6 6 53 5 4 -0 -2 6 3 -8 -8 10 3 3 -8 6 1 -4 -5 -5 4 -3 -6 -2 2 5 7 -5 -5 5 -3 -5 -4 -2 2 -0 -6 -4 -1 7 -2 -7 -4 -6 -24 4 5 7 9 3 -9 2 8 -10 6 5 -6 4 3 -9 -6 -6 -1 -7 -9 -6 -9 3 -6 -0 1 -10 3 6 5 2 5 -4 3 6 -6 -10 2 3 -8 -5 -16 -5 -0 -1 -8 -7 -5 1 -0 -8 -1 -2 -1 4 -4 -2 1 1 10 2 2 -22 9 -0 4 -4 3 9 3 3 -4 -3 -7 3 -9 8 8 -5 -4 -4 -8 -4 -1 1 -9 -4 3 -3 2 -8 5 0 -2 8 -2 -4 3 -2 -5 2 9 -0 10 5 -6 -4 4 7 -5 4 -9 1 4 -8 5 4 -7 -8 -5 -7 5 -9 9 6 -16 5 -9 -1 -10 3 -4 9 -8 -8 10 -7 -4 5 -2 -5 10 9 5 4 9 10 6 -0 -5 -3 2 9 2 6 -1 -2 6 -2 -3 -5 1 4 -5 -1 -2 -5 2 -5 9 1 8 1 2 2 -1 -7 -4 -4 6 7 -7 1 -3 -4 2 -5 -4 -5 3 3 -2 6 -1 -8 -4 3 2 -4 4 7 -6 4 -6 -0 8 9 4 9 34 -3 -0 6 -6 0 -2 -9 6 9 2 -1 -6 7 -8 5 -3 5 5 6 -4 10 -6 1 9 -8 5 5 -0 8 6 8 -2 -6 -9 1 -8 10 4 -3 1 9 26 -3 6 -5 -1 5 -4 6 -6 -5 7 9 4 5 8 8 4 -5 -3 1 -7 25 1 -4 3 -5 1 2 -2 -0 10 -5 -4 -1 -10 3 -8 0 -5 -7 6 7 -18 9 0 5 9 1 8 4 2 8 2 2 0 3 6 8 9 4 9 6 6 1040 r= 6.937584706448451e+02 1.114511464689273e+03 3.275601686175421e+02 1.234106403960968e+03 1.213446859536208e+03 4.764898686657967e+02 1.922261317490563e+03 8.754734793689248e+02 9.613179907728340e+01 9.158252783516164e+02 1.400905897212578e+03 2.368144419926755e+03 5.277992910496147e+02 -1.566035859056928e+02 1.723517320192720e+03 2.772283458029889e+03 1.097056411066004e+03 -1.853144212915592e+02 1.363547624392920e+03 1.641121501940453e+03 s= -1.457324021164642e+04 Q= -316 39 -78 162 -73 -113 -60 111 33 -32 138 -15 94 -102 -73 -143 50 -15 25 -55 39 -519 -119 11 -51 6 -57 -138 26 153 75 -226 -47 196 -75 77 102 85 256 218 -78 -119 -259 109 59 -126 39 -28 -80 160 171 -65 35 231 -96 -14 53 134 -35 66 162 11 109 -563 25 -56 61 8 -72 121 -321 -105 -51 -58 51 156 -24 -71 -109 -27 -73 -51 59 25 -309 -53 -144 49 -68 -152 -98 -69 -11 -105 57 -4 -57 126 -22 -44 -113 6 -126 -56 -53 -363 16 9 22 100 24 -48 108 49 -137 37 136 156 9 8 -60 -57 39 61 -144 16 -636 108 391 -40 180 -98 -9 26 143 -55 -133 158 195 50 111 -138 -28 8 49 9 108 -372 -34 124 -100 -152 172 27 -94 119 -58 -1 64 -83 33 26 -80 -72 -68 22 391 -34 -737 -23 -267 133 -67 -121 -7 57 114 3 -292 -0 -32 153 160 121 -152 100 -40 124 -23 -410 -52 195 -270 -188 -112 -240 -28 -186 -68 -8 138 75 171 -321 -98 24 180 -100 -267 -52 -476 -29 2 -134 100 131 -130 -62 -178 -176 -15 -226 -65 -105 -69 -48 -98 -152 133 195 -29 -473 283 89 10 -16 -83 295 -19 -197 94 -47 35 -51 -11 108 -9 172 -67 -270 2 283 -589 95 -156 -124 59 -341 27 285 -102 196 231 -58 -105 49 26 27 -121 -188 -134 89 95 -549 -62 -37 128 -110 32 -37 -73 -75 -96 51 57 -137 143 -94 -7 -112 100 10 -156 -62 -517 -196 234 -106 65 188 -143 77 -14 156 -4 37 -55 119 57 -240 131 -16 -124 -37 -196 -496 42 -95 -169 -164 50 102 53 -24 -57 136 -133 -58 114 -28 -130 -83 59 128 234 42 -424 -21 -159 -253 -15 85 134 -71 126 156 158 -1 3 -186 -62 295 -341 -110 -106 -95 -21 -685 64 13 25 256 -35 -109 -22 9 195 64 -292 -68 -178 -19 27 32 65 -169 -159 64 -500 -309 -55 218 66 -27 -44 8 50 -83 -0 -8 -176 -197 285 -37 188 -164 -253 13 -309 -585 best found x= 1.205040578053683E+00 1.494674949355039E+00 0.000000000000000E+00 5.359016277531363E-01 0.000000000000000E+00 2.549197810546648E+00 2.612323958509321E-02 1.758016214036641E+00 1.073100354194154E+00 0.000000000000000E+00 1.452516329400301E-01 1.416177425004463E+00 3.384627665455049E+00 2.911182944268297E+00 0.000000000000000E+00 1.450273005710060E+00 2.542415745649929E+00 0.000000000000000E+00 1.012805393049647E+00 1.060167546104215E+00