Steve Jacobsen (jacobsen@ee.ucla.edu), Khosrow Moshirvaziri (moshir@ee.ucla.edu) LINEAR REVERSE CONVEX MINIMIZATION PROBLEM (m=10,n=40): min cx Ax < b x > 0 g(x) < 0 where g(x) = xQx + rx + s A= -6 1 1 -3 -9 -7 -0 -1 3 7 1 7 4 -2 -2 3 8 -3 -6 -1 -4 4 -0 10 -6 -2 3 -4 6 -8 2 4 1 -2 9 -7 8 4 -10 0 -9 3 -8 3 3 -0 -5 9 5 -2 6 -7 9 -0 -7 -7 -1 -5 4 9 1 6 3 -6 10 4 -6 6 -7 -6 -5 -7 -4 -4 -1 3 -5 4 -0 -9 4 -10 3 5 8 8 -8 -9 5 7 -9 -6 -5 -7 1 3 -7 -7 8 3 0 4 4 -1 -7 4 -6 6 -2 3 -4 -7 2 -8 9 -3 9 -1 -8 1 4 -2 -2 10 -5 8 9 5 10 -5 1 4 -6 2 -5 2 9 6 -5 -1 -8 5 -6 -4 3 -6 -8 -2 2 4 4 -0 0 -3 -4 1 -5 2 -7 -2 9 -9 4 -3 -1 -9 -9 5 8 -2 -0 -7 -4 7 -0 6 -2 -1 7 6 -2 -10 8 0 2 7 -2 -4 -6 6 -8 7 -1 -5 -1 0 7 5 8 -6 -2 -2 8 -5 5 8 0 7 -5 1 9 -8 8 2 -1 -5 -7 -3 -1 4 2 8 7 8 -10 4 9 -6 7 4 5 6 -5 3 0 7 4 10 6 -2 0 4 5 10 -0 0 -2 -7 -4 -1 5 -5 3 9 9 -0 8 -1 0 4 8 0 8 -1 -10 7 9 -10 -7 5 1 1 -3 4 3 -10 -1 4 5 3 7 2 -5 4 -5 0 -4 -10 -3 -4 1 -10 -7 1 -7 -2 -8 6 2 10 -1 -1 1 -1 5 -8 -2 -6 10 3 1 5 -2 0 -2 -5 6 -4 -1 3 -9 9 -9 5 -5 -4 8 4 0 -6 8 -2 4 -7 -6 -6 -7 9 6 9 5 -9 -7 6 5 -8 -5 10 -5 3 2 -4 -1 5 2 3 -10 5 -10 4 3 8 4 7 3 0 1 5 8 2 1 1 2 7 3 1 5 5 5 5 2 3 8 7 6 7 3 1 10 6 0 9 0 4 5 6 7 7 5 1 b= 6 -22 -19 8 16 80 54 -29 -6 1750 c= 9 -6 -3 2 2 -7 1 9 -3 7 9 -5 -5 -2 6 8 -5 5 4 -1 -5 3 -8 -6 -8 1 -10 -6 2 -1 -8 4 -2 7 -8 9 -9 -8 -0 5 Q= -244 161 -48 -82 -128 -63 56 -36 -49 -87 44 58 159 -54 -115 -141 -7 1 -47 69 96 -113 7 183 59 -98 128 89 -43 -50 112 -35 -3 8 109 -92 10 136 -93 -12 161 -307 52 -66 122 113 -128 -59 -9 139 -117 -75 -144 -101 30 115 -113 -148 4 -106 -131 137 -39 -154 -179 32 -136 -46 -3 -47 -94 -78 18 -129 -45 12 64 -155 -42 -24 -48 52 -210 21 -116 -122 123 60 21 -82 26 71 -67 -131 -96 -2 -51 141 26 -4 -46 -154 -239 -66 160 -186 -205 148 -96 -50 -33 -96 33 26 -85 42 -217 -104 -163 41 -82 -66 21 -338 8 -67 -79 24 -151 53 -32 34 83 -81 -59 -44 -136 -129 -86 -106 -31 -0 -10 58 -14 -27 98 3 64 -164 7 16 7 -28 -37 44 78 -51 75 -62 -128 122 -116 8 -234 -133 144 40 44 -73 60 168 30 -14 -97 -11 168 94 -131 -26 -57 -71 -140 59 90 -163 -24 -5 -14 -97 71 7 17 15 -0 -90 -98 24 -156 -1 -63 113 -122 -67 -133 -306 31 48 -80 50 94 86 33 -32 44 53 33 82 -6 -26 5 -123 -124 28 34 -55 -29 -14 -20 -139 -74 48 13 119 -25 -14 -111 -96 -38 75 56 -128 123 -79 144 31 -216 -177 -63 138 -145 -74 -9 -5 110 45 -65 -194 52 -35 51 53 158 -23 -141 156 89 -29 -20 -31 -74 -35 20 -80 101 -92 197 -57 84 -6 -36 -59 60 24 40 48 -177 -328 -8 32 -231 2 -27 -15 57 2 53 -188 13 -21 93 -47 133 -47 -62 73 84 41 -168 -27 -18 -159 55 -155 170 -281 165 -40 -39 -12 -49 -9 21 -151 44 -80 -63 -8 -249 -0 116 -114 94 5 76 -53 -137 -60 -5 -9 103 -57 19 -23 -139 41 128 -94 -95 -42 -21 -3 -56 96 -84 -0 -86 -41 150 24 -87 139 -82 53 -73 50 138 32 -0 -215 40 37 27 38 -92 -121 36 111 -40 32 55 -120 -59 -28 180 -110 15 72 -96 69 98 -54 -11 29 -85 1 -160 55 20 -25 44 -117 26 -32 60 94 -145 -231 116 40 -336 92 -119 -59 -29 42 39 -156 3 -95 -43 -3 59 -83 106 21 -48 137 -42 -51 -36 -139 103 -221 112 -145 201 -100 -59 -64 58 -75 71 34 168 86 -74 2 -114 37 92 -221 26 -6 92 -24 -194 -36 129 89 99 34 82 -26 -178 111 29 -37 -51 110 -45 -14 -62 63 -19 78 -27 21 98 45 159 -144 -67 83 30 33 -9 -27 94 27 -119 26 -196 -54 12 117 12 19 28 -82 -121 15 -124 -198 45 -38 -225 40 -47 -5 -95 -84 49 -79 -82 14 -65 -175 -75 7 -54 -101 -131 -81 -14 -32 -5 -15 5 38 -59 -6 -54 -245 -117 -0 -203 -14 71 3 -57 -68 -167 -5 20 -138 -195 191 -58 -79 -53 -145 42 -75 25 36 -47 -89 -224 19 -115 30 -96 -59 -97 44 110 57 76 -92 -29 92 12 -117 -194 -79 -38 46 -49 3 -64 -44 -117 69 150 -172 -79 153 22 -34 84 -63 28 -68 7 37 -32 50 -161 -49 -141 115 -2 -44 -11 53 45 2 -53 -121 42 -24 117 -0 -79 -149 -63 12 -2 73 106 -75 49 98 71 -37 117 75 -37 47 99 -26 -24 21 25 3 -16 124 33 -26 -7 -113 -51 -136 168 33 -65 53 -137 36 39 -194 12 -203 -38 -63 -407 -29 179 67 54 -56 -62 -10 -53 -16 -103 165 -50 23 -79 -100 -22 26 -48 191 -70 -59 -6 35 1 -148 141 -129 94 82 -194 -188 -60 111 -156 -36 19 -14 46 12 -29 -236 -34 -61 20 85 156 11 -160 109 131 -51 -9 -62 -8 -47 18 -131 114 -139 228 -13 44 -50 -47 4 26 -86 -131 -6 52 13 -5 -40 3 129 28 71 -49 -2 179 -34 -204 -106 -82 52 -21 9 -3 -61 90 -129 41 -92 89 49 -1 -38 -43 -90 16 19 10 -69 69 -106 -4 -106 -26 -26 -35 -21 -9 32 -95 89 -82 3 3 73 67 -61 -106 -151 -112 34 -63 -114 15 -26 -39 -61 11 -107 -32 -8 34 -67 -85 -33 10 -135 28 -45 96 -131 -46 -31 -57 5 51 93 103 55 -43 99 -121 -57 -64 106 54 20 -82 -112 -202 94 -147 -74 23 -89 -173 -22 97 -80 -28 18 33 -68 -80 64 -17 -99 -108 -33 -113 137 -154 -0 -71 -123 53 -47 -57 -120 -3 34 15 -68 -44 -75 -56 85 52 34 94 -221 -105 -29 168 -106 -44 155 -163 -20 -10 -111 25 43 -25 -39 -159 -54 -46 40 7 -39 -239 -10 -140 -124 158 133 19 -59 59 82 -124 -167 -117 49 -62 156 -21 -63 -147 -105 -343 -130 119 -240 -298 100 -72 -91 -53 -90 28 20 -174 94 -284 -171 -202 34 183 -154 -66 58 59 28 -23 -47 -23 -28 -83 -26 -198 -5 69 98 -10 11 9 -114 -74 -29 -130 -304 15 -20 -182 -27 -145 6 -107 -109 23 -36 -189 -1 -167 -236 46 11 59 -179 160 -14 90 34 -141 -62 -139 180 106 -178 45 20 150 71 -53 -160 -3 15 23 168 119 15 -419 150 107 -240 -3 -8 -42 43 -71 18 55 -75 92 20 35 37 -98 32 -186 -27 -163 -55 156 73 41 -110 21 111 -38 -138 -172 -37 -16 109 -61 -26 -89 -106 -240 -20 150 -236 -168 129 -59 -72 41 -94 29 -25 -74 19 -179 -45 -204 -9 128 -136 -205 98 -24 -29 89 84 128 15 -48 29 -225 -195 -79 117 -103 131 90 -39 -173 -44 -298 -182 107 -168 -406 163 -49 -20 -122 -124 56 -46 -117 125 -198 -204 -238 48 89 -46 148 3 -5 -14 -29 41 -94 72 137 -37 40 191 153 75 165 -51 -129 -61 -22 155 100 -27 -240 129 163 -329 64 -10 12 159 -70 80 -69 -48 21 21 175 -3 -43 -3 -96 64 -14 -20 -20 -168 -95 -96 -42 -51 -47 -58 22 -37 -50 -9 41 11 97 -163 -72 -145 -3 -59 -49 64 -272 10 -30 -191 11 -20 -31 -148 -157 -101 -49 41 -50 -47 -50 -164 -97 -139 -31 -27 -42 69 -51 110 -5 -79 -34 47 23 -62 -92 -107 -80 -20 -91 6 -8 -72 -20 -10 10 -177 -27 -14 38 -44 2 -65 25 -98 -77 -15 112 -94 -33 7 71 -74 -74 -18 -21 98 -36 -45 -95 -53 84 99 -79 -8 89 -32 -28 -10 -53 -107 -42 41 -122 12 -30 -27 -130 -27 20 11 -37 39 -31 -148 1 51 -35 -78 -96 16 7 48 -35 -159 -3 -54 -139 -14 -84 -145 -63 -26 -100 -47 49 -8 18 -111 -90 -109 43 -94 -124 159 -191 -14 -27 -216 47 -114 19 -103 -59 -98 -142 3 -3 18 33 7 17 13 20 55 -56 -11 103 -62 49 42 28 -24 -22 18 -1 34 33 25 28 23 -71 29 56 -70 11 38 20 47 -44 64 -32 39 -37 49 61 11 8 -129 26 -28 15 119 -80 -155 96 29 -221 63 -79 -75 -68 21 26 -131 -38 -67 -68 43 20 -36 18 -25 -46 80 -20 -44 11 -114 64 -193 92 -118 150 -37 -113 -63 109 -45 -85 -37 -0 -25 101 170 -84 -85 112 -19 -82 25 7 25 -48 114 -43 -85 -80 -25 -174 -189 55 -74 -117 -69 -31 2 -37 19 -32 92 -281 160 -257 -140 114 1 -92 12 42 44 -90 -14 -92 -281 -0 1 -145 78 14 36 37 3 191 -139 -90 -33 64 -39 94 -1 -75 19 125 -48 -148 -65 39 -103 39 -118 160 -335 119 8 -79 -14 10 64 -217 78 -98 -111 197 165 -86 -160 201 -27 -65 -47 -32 -16 -70 228 16 10 -17 -159 -284 -167 92 -179 -198 21 -157 25 -31 -59 -37 150 -257 119 -417 -120 -37 70 136 -155 -104 -51 24 -96 -57 -40 -41 55 -100 21 -175 -89 50 124 -59 -13 19 -135 -99 -54 -171 -236 20 -45 -204 21 -101 -98 -148 -98 49 -37 -140 8 -120 -276 -19 26 -93 -42 -163 75 -156 -38 84 -39 150 20 -59 98 -75 -224 -161 33 -6 44 10 28 -108 -46 -202 46 35 -204 -238 175 -49 -77 1 -142 61 -113 114 -79 -37 -19 -399 26 -12 -24 41 -62 -1 75 -6 -12 24 -25 -64 45 7 19 -49 -26 35 -50 -69 -45 -33 40 34 11 37 -9 48 -3 41 -15 51 3 11 -63 1 -14 70 26 26 -61 r= -1.960708975774579e+05 1.744522481478295e+05 4.436129313902191e+04 -1.172565873731852e+05 -5.027196283728206e+04 1.276708088827654e+05 -4.372826982306663e+04 -2.354211178305825e+05 1.165282673370884e+05 -1.868060180072551e+05 -3.448702589184009e+05 2.265441256751045e+05 7.813654585883545e+04 6.128458082553276e+04 -1.641424979761394e+05 -1.795772779502504e+05 1.636737223736562e+05 -1.217344804403495e+05 -1.144811130255056e+05 -5.170728201746325e+04 8.944228636008555e+04 -1.211633448613907e+05 1.829749650120136e+05 1.049672092758694e+05 3.714467012334287e+05 -3.359516314578238e+04 2.257380442448116e+05 2.193933587232711e+05 -1.874018740338950e+04 -2.555428271035318e+04 1.713732936851640e+05 -9.750211338997907e+04 1.018651969538518e+05 -2.087931817817763e+05 1.700956064911997e+05 -2.059741037322734e+05 2.582952578322070e+05 1.195022133199797e+05 5.410973460110273e+04 -1.551086363099405e+05 s=-1.868410008913403e+08 optimal x = x(6)= 9.928245230073556e+01 x(21)= 3.305457349837847e+02 x(25)= 7.399759345728499e-01 x(28)= 2.505126642486300e+01 x(31)= 7.646240634654025e+02 x(33)= 1.201788873775498e+03 x(37)= 6.889103830186990e+01 x(39)= 1.154360279774085e+02 all other x's = 0.0