Steve Jacobsen (jacobsen@ee.ucla.edu), K. Moshirvaziri (moshir@ee.ucla.edu) CONCAVE MININIMIZATION PROBLEM (m=21, n=50): min f(x) Ax < b x > 0 where f(x) = -(e'x)**1.5 , where e'=(1,1/2,2/3,3/4,4/5,...,(n-1)/n) A= -1 -6 0 4 -5 0 -4 -4 2 5 -10 6 10 -4 7 -7 6 7 5 -3 5 5 2 -6 -8 -4 -8 -6 8 -9 -3 -3 -5 4 -1 4 -7 -6 -7 -1 4 8 10 0 -3 -1 6 9 -1 3 2 -3 9 -4 9 -7 6 2 -4 1 5 5 -5 9 -6 5 -4 -4 7 5 4 -1 -8 -6 7 3 8 3 1 1 8 1 0 7 4 -3 -2 7 -3 -10 6 -3 -1 7 0 1 -7 4 0 5 -1 1 3 4 0 6 -4 -8 -9 -8 -8 3 9 -1 -6 -3 8 -1 2 3 -5 2 0 -9 -3 4 2 -3 -7 -7 7 -6 9 -10 6 -7 -8 5 -7 -3 2 -4 9 -1 -1 -4 7 -6 2 -3 1 1 0 -1 -8 6 -4 5 0 6 -4 -2 1 -4 4 7 3 -9 6 -1 -5 9 9 -5 -6 4 -9 -1 4 6 -1 1 2 1 2 -5 -3 -3 9 -9 -9 -3 1 0 6 -7 3 -5 -10 10 -1 -10 1 -5 -4 -5 -2 3 6 -1 0 6 -5 -3 -1 -6 -8 -6 8 -10 -5 5 4 2 5 3 9 -3 -8 -3 3 8 3 -5 4 -7 -5 -1 5 8 -5 -1 8 -6 -7 -6 5 -2 -7 3 -4 4 6 1 3 3 -2 -2 -2 3 4 2 4 -10 2 7 -2 -2 -5 3 -6 -3 -2 -4 -7 6 0 3 1 3 3 -4 1 -1 5 -2 -5 -6 -2 3 -8 -10 -9 -6 -5 -9 5 7 0 9 -1 -3 -4 -2 7 1 -2 -9 -3 6 -8 -1 3 -3 1 -9 -5 8 7 -2 0 -3 -5 10 -5 2 9 8 -7 7 1 -2 -1 4 7 -7 -6 -2 -6 4 9 2 -5 -5 -6 5 9 -5 -5 6 2 -7 6 6 -10 -7 3 6 -8 8 -1 -3 2 -4 0 5 -7 -2 -6 8 9 -7 4 6 -10 -2 -8 -9 4 -7 -8 -7 -5 4 1 1 -5 -8 -7 -9 4 7 10 -7 -2 5 -4 0 -7 -7 5 1 -6 9 -3 3 5 -8 -1 -6 -7 -2 5 -5 7 -10 4 -5 -10 -3 10 -4 6 9 -4 -9 -9 8 4 -7 -3 0 -8 1 -5 -6 -8 8 9 10 -1 8 4 -10 7 8 5 -5 10 -7 2 -6 -10 -5 8 -3 -9 -3 2 0 2 -8 5 10 9 -2 -8 -5 1 -5 9 8 1 -5 2 -10 10 8 -1 8 -2 6 1 7 -5 7 8 -5 5 3 -3 2 -9 2 3 -2 -2 -6 6 5 4 -9 -2 3 6 -5 -10 -7 -7 -7 9 10 -2 -8 -1 8 1 1 -5 -2 4 3 1 -4 7 10 -5 9 -6 9 0 2 4 -7 5 -1 -6 3 1 -10 -7 2 2 9 -7 7 0 -4 -6 -3 -9 4 1 3 -6 3 -5 -8 0 4 6 -2 -7 0 -2 -4 8 1 -5 -6 8 7 6 9 8 9 -5 9 -4 3 -6 10 -3 2 2 -3 7 10 1 7 -1 9 0 -7 10 1 9 4 6 7 -5 4 7 10 -8 2 9 -3 1 -9 -5 -4 8 -6 -5 6 3 -6 -7 2 -8 2 3 -4 -2 -3 -3 8 3 5 7 1 3 8 6 5 3 -2 6 -5 3 4 -9 0 6 3 4 9 -4 -9 9 5 -9 -10 -1 1 2 2 2 9 10 -4 5 -4 -2 6 -5 5 10 1 4 0 0 9 7 8 -5 -2 -1 9 4 -2 -4 4 10 -6 2 8 -6 3 -6 4 8 -7 -9 7 -9 10 5 5 1 5 5 10 -5 -1 4 3 3 7 0 2 -7 -1 6 2 -7 -8 4 -4 -7 0 6 -7 1 8 -5 -1 -4 4 6 -4 -10 5 7 -4 -7 -4 1 -7 -6 2 5 2 -9 6 7 3 7 -2 -6 3 1 2 10 0 -4 1 -8 4 4 8 6 3 -6 9 1 8 -3 2 -1 1 5 7 2 -6 1 5 -4 -6 8 0 1 -5 -2 8 -9 3 -5 -5 0 -9 -5 7 4 3 -6 -7 8 2 5 0 0 7 8 5 9 3 -5 -6 6 7 -4 -2 4 1 7 -8 0 5 3 6 -8 4 -9 7 3 -3 0 2 -9 -9 -8 -8 9 6 -5 -7 -5 -3 -1 2 -4 9 -6 9 -2 2 8 -3 6 0 7 -2 -6 5 2 -8 8 -6 7 -5 4 4 3 4 8 7 -3 9 10 -3 -8 8 0 2 -10 10 5 -1 -1 -2 8 -6 10 -7 7 8 -9 2 -1 -10 6 -1 7 -10 6 2 -6 -9 -5 -9 7 -4 4 1 -8 -9 6 10 2 -7 -1 -4 4 1 -8 -5 10 -5 -4 -4 2 -10 -6 -2 7 -1 8 -6 -7 -8 5 2 -7 2 -4 -2 0 1 2 -9 -8 3 8 -9 9 -9 -5 -1 3 -4 -6 -4 -10 -10 -2 9 0 10 10 8 -2 -2 -9 -4 3 -6 4 -4 9 -7 -7 0 10 3 -4 9 -4 1 -3 -7 -3 7 -9 -10 -8 6 6 6 0 3 0 4 -9 4 -5 3 0 -1 3 5 3 1 1 9 10 9 8 4 4 9 1 4 4 4 8 4 1 7 10 9 8 6 1 3 2 5 1 9 7 5 5 5 4 7 10 5 1 7 7 10 7 4 6 10 9 5 9 6 b= 5 65 -38 1 -32 -23 3 -66 -3 32 -3 95 42 92 23 40 29 58 -67 -18 2860 best found x = x( 1) = 3.375835983499439E+01 x( 2) = 5.791872201822221E+00 x( 3) = 1.813170134635393E+01 x( 4) = 7.477545236917588E+01 x( 8) = 2.379099065458087E+01 x(14) = 4.342463653370791E+00 x(18) = 3.254606680076729E+02 x(19) = 5.790875617794892E+01 x(25) = 9.089166144418940E+01 x(26) = 6.094074156505175E+01 x(27) = 1.154223089485486E+02 x(29) = 1.831347983703217E+02 x(39) = 3.216615019575511E+02 all other x's = 0.0