Steve Jacobsen (jacobsen@ee.ucla.edu), Khosrow Moshirvaziri (moshir@ee.ucla.edu) LINEAR REVERSE CONVEX MINIMIZATION PROBLEM (m=25, n=20): min cx Ax < b x > 0 g(x) < 0 where g(x) = xQx + rx + s, and g is concave. A,b = -6 8 -7 7 1 8 3 -3 -4 7 -2 -6 2 -5 -7 10 -4 4 7 -8 25 -9 5 -0 -7 6 3 -7 -1 1 8 4 -10 -5 -3 3 4 6 -3 9 9 32 4 -5 8 -10 -9 -7 3 6 0 1 4 -6 -4 -2 -3 -4 -3 -9 -5 -9 -31 4 -9 8 4 1 4 2 9 -8 -7 -6 10 4 -1 1 5 4 10 -5 -8 39 9 5 -9 7 -0 -2 6 3 -2 -1 7 -5 -8 -0 0 -7 -4 1 -2 -0 18 -2 -3 8 3 9 -2 -5 -6 2 10 4 6 5 -2 7 -10 -10 -10 6 5 34 0 3 0 5 5 -0 -0 4 8 -6 7 -7 1 -4 -10 -0 -8 7 8 9 39 7 5 0 5 1 -7 -2 8 -1 -1 -8 -2 1 -8 -5 -8 0 -9 -5 -5 -16 -9 10 -4 10 8 2 -6 -5 5 -4 -8 2 2 -3 3 -7 6 -2 5 -3 20 -9 -3 10 8 2 7 -9 7 7 0 5 -6 -3 -5 1 8 -6 -0 4 5 43 1 -5 -0 -5 7 2 8 -1 4 8 3 7 4 3 8 6 -9 2 -1 -0 60 3 10 -5 -4 -7 9 -1 0 6 -1 -6 -7 -7 4 -5 5 -9 5 -5 5 10 -10 4 -8 -3 -6 1 -7 2 4 -1 -6 10 -7 0 9 -1 -7 4 3 3 6 -2 5 9 0 4 -7 9 6 5 6 -8 -5 -0 5 -5 -10 4 1 -8 4 32 -9 3 -9 2 -7 10 -2 5 -10 -3 -2 -5 7 4 7 2 -4 -9 -6 5 -1 -2 -9 0 7 -8 -2 -7 -1 8 -6 9 -8 6 9 4 0 -9 -8 -8 -9 -13 4 3 -2 -2 -5 -7 8 9 0 10 9 -6 1 -1 -1 -9 -0 9 1 -5 36 2 8 -4 7 -10 1 -8 3 -1 -7 -2 3 5 9 6 1 -1 -6 -10 -6 8 9 -5 8 -5 -2 -5 -7 -1 -9 3 -5 4 -4 -4 -10 -2 0 -3 -6 1 -21 7 -1 1 -2 -9 -0 -9 6 4 2 4 6 -7 -1 -7 -6 -1 2 2 3 14 1 5 -1 1 4 -1 -3 4 -0 -10 -4 4 1 0 4 -2 -7 2 -1 2 18 -8 -0 9 -1 9 9 -5 4 3 -10 6 5 -4 3 4 3 -4 -7 -8 -3 24 3 -5 -9 -4 -5 -7 -7 10 4 5 6 3 2 -2 -1 3 7 1 4 -6 20 -2 -5 5 -6 -6 -6 6 9 -6 5 -2 3 0 2 2 4 4 9 -2 -5 28 2 7 2 1 7 1 10 5 6 9 0 6 7 5 1 5 5 8 1 5 1120 c= -1 -3 -1 5 -6 -7 -3 9 9 -5 -9 -8 1 -7 0 -8 7 -3 -2 -3 Q= -418 177 61 -8 278 142 -115 -129 93 34 -91 -136 45 -67 59 106 105 -131 131 10 177 -428 198 -203 -56 -37 100 107 -75 -43 14 232 38 -16 60 92 -15 113 -99 -28 61 198 -390 164 -123 -7 -27 -161 -33 81 62 -161 -18 -81 -5 4 -68 -26 191 -43 -8 -203 164 -392 52 -10 28 -68 -16 220 150 53 -72 56 74 111 -17 -47 29 196 278 -56 -123 52 -491 -145 -141 105 -69 -58 -68 37 4 39 -61 -104 62 -30 -119 -99 142 -37 -7 -10 -145 -281 92 75 111 42 -119 -129 -7 3 -56 -278 110 -6 -63 115 -115 100 -27 28 -141 92 -458 15 70 -190 27 38 -61 -34 44 -25 126 -170 66 4 -129 107 -161 -68 105 75 15 -321 -80 165 53 -21 33 -5 74 134 -39 -65 189 21 93 -75 -33 -16 -69 111 70 -80 -323 28 11 135 31 52 57 211 4 76 -46 -164 34 -43 81 220 -58 42 -190 165 28 -494 -26 146 42 22 46 -81 18 -52 -198 -147 -91 14 62 150 -68 -119 27 53 11 -26 -428 7 172 -28 26 -135 272 5 -113 -188 -136 232 -161 53 37 -129 38 -21 135 146 7 -522 -88 -160 -175 -109 76 -40 227 202 45 38 -18 -72 4 -7 -61 33 31 42 172 -88 -222 -36 -66 -113 -3 -47 55 132 -67 -16 -81 56 39 3 -34 -5 52 22 -28 -160 -36 -234 -128 -2 64 88 249 31 59 60 -5 74 -61 -56 44 74 57 46 26 -175 -66 -128 -359 -84 -41 170 166 113 106 92 4 111 -104 -278 -25 134 211 -81 -135 -109 -113 -2 -84 -486 167 -72 -104 112 105 -15 -68 -17 62 110 126 -39 4 18 272 76 -3 64 -41 167 -348 69 17 26 -131 113 -26 -47 -30 -6 -170 -65 76 -52 5 -40 -47 88 170 -72 69 -283 -111 -6 131 -99 191 29 -119 -63 66 189 -46 -198 -113 227 55 249 166 -104 17 -111 -485 -186 10 -28 -43 196 -99 115 4 21 -164 -147 -188 202 132 31 113 112 26 -6 -186 -378 r= 3.774344531513882e+03 -1.022284538920139e+03 -8.475204289831322e+02 -5.542168041708737e+03 1.634728712857385e+03 9.239557922616641e+02 4.687416544369568e+03 -7.041745363141887e+03 -6.766698697954762e+03 7.079000174055321e+03 4.403412101865543e+03 4.401620125000029e+03 1.043108772011788e+03 3.860241745943957e+03 3.919460776610798e+02 5.034391889751902e+03 -3.313593145014338e+03 4.219011004005938e+03 3.348573257560337e+03 3.899843489869375e+03 s=-7.699029976983108e+04 optimal x = 5.006530074189694e+00 5.285134728411564e+00 6.525308428750026e+00 3.828772433114229e+00 0 9.829348894109215e+00 7.413439244866242e+00 0 0 0 4.004274524443275e+00 4.379866582792696e+00 0 1.686792811942252e+01 0 0 6.489082723484133e+00 0 1.327713551349816e+01 2.199685357246413e+00