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## st_qpc-m3a.gms:

#### References:

• Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
• Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, 1999. PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne

Point:

* NLP written by GAMS Convert at 08/31/02 19:13:01 * * Equation counts * Total E G L N X C * 11 1 0 10 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 11 11 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 108 98 10 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11; e1.. 20*x1 + 20*x2 + 60*x3 + 60*x4 + 60*x5 + 60*x6 + 5*x7 + 45*x8 + 55*x9 + 65*x10 =L= 600.1; e2.. 5*x1 + 7*x2 + 3*x3 + 8*x4 + 13*x5 + 13*x6 + 2*x7 + 14*x8 + 14*x9 + 14*x10 =L= 310.5; e3.. 100*x1 + 130*x2 + 50*x3 + 70*x4 + 70*x5 + 70*x6 + 20*x7 + 80*x8 + 80*x9 + 80*x10 =L= 1800; e4.. 200*x1 + 280*x2 + 100*x3 + 200*x4 + 250*x5 + 280*x6 + 100*x7 + 180*x8 + 200*x9 + 220*x10 =L= 3850; e5.. 2*x1 + 2*x2 + 4*x3 + 4*x4 + 4*x5 + 4*x6 + 2*x7 + 6*x8 + 6*x9 + 6*x10 =L= 18.6; e6.. 4*x1 + 8*x2 + 2*x3 + 6*x4 + 10*x5 + 10*x6 + 5*x7 + 10*x8 + 10*x9 + 10*x10 =L= 198.7; e7.. 60*x1 + 110*x2 + 20*x3 + 40*x4 + 60*x5 + 70*x6 + 10*x7 + 40*x8 + 50*x9 + 50*x10 =L= 882; e8.. 150*x1 + 210*x2 + 40*x3 + 70*x4 + 90*x5 + 105*x6 + 60*x7 + 100*x8 + 140*x9 + 180*x10 =L= 4200; e9.. 80*x1 + 100*x2 + 6*x3 + 16*x4 + 20*x5 + 22*x6 + 20*x8 + 30*x9 + 30*x10 =L= 40.25; e10.. 40*x1 + 40*x2 + 12*x3 + 20*x4 + 24*x5 + 28*x6 + 40*x9 + 50*x10 =L= 327; e11.. - (10*x1 - 6.8*x1*x1 - 4.6*x1*x2 + 10*x2 - 7.9*x1*x3 + 10*x3 - 5.1*x1*x4 + 10*x4 - 6.9*x1*x5 + 10*x5 - 6.8*x1*x6 + 10*x6 - 4.6*x1*x7 + 10*x7 - 7.9*x1*x8 + 10*x8 - 5.1*x1*x9 + 10*x9 - 6.9*x1*x10 + 10*x10 - 4.6*x2*x1 - 5.5*x2*x2 - 5.8*x2*x3 - 4.5*x2*x4 - 6*x2*x5 - 4.6*x2*x6 - 5.5*x2*x7 - 5.8*x2*x8 - 4.5*x2*x9 - 6*x2*x10 - 7.9*x3*x1 - 5.8*x3*x2 - 13.3*x3*x3 - 6.7*x3*x4 - 8.9*x3*x5 - 7.9*x3*x6 - 5.8*x3*x7 - 13.3*x3*x8 - 6.7*x3*x9 - 8.9*x3*x10 - 5.1*x4*x1 - 4.5*x4*x2 - 6.7*x4*x3 - 6.9*x4*x4 - 5.8*x4*x5 - 5.1*x4*x6 - 4.5*x4*x7 - 6.7*x4*x8 - 6.9*x4*x9 - 5.8*x4*x10 - 6.9*x5*x1 - 6*x5*x2 - 8.9*x5*x3 - 5.8*x5*x4 - 11.9*x5*x5 - 6.9*x5*x6 - 6*x5*x7 - 8.9* x5*x8 - 5.8*x5*x9 - 11.9*x5*x10 - 6.8*x6*x1 - 4.6*x6*x2 - 7.9*x6*x3 - 5.1 *x6*x4 - 6.9*x6*x5 - 6.8*x6*x6 - 4.6*x6*x7 - 7.9*x6*x8 - 5.1*x6*x9 - 6.9* x6*x10 - 4.6*x7*x1 - 5.5*x7*x2 - 5.8*x7*x3 - 4.5*x7*x4 - 6*x7*x5 - 4.6*x7 *x6 - 5.5*x7*x7 - 5.8*x7*x8 - 4.5*x7*x9 - 6*x7*x10 - 7.9*x8*x1 - 5.8*x8* x2 - 13.3*x8*x3 - 6.7*x8*x4 - 8.9*x8*x5 - 7.9*x8*x6 - 5.8*x8*x7 - 13.3*x8 *x8 - 6.7*x8*x9 - 8.9*x8*x10 - 5.1*x9*x1 - 4.5*x9*x2 - 6.7*x9*x3 - 6.9*x9 *x4 - 5.8*x9*x5 - 5.1*x9*x6 - 4.5*x9*x7 - 6.7*x9*x8 - 6.9*x9*x9 - 5.8*x9* x10 - 6.9*x10*x1 - 6*x10*x2 - 8.9*x10*x3 - 5.8*x10*x4 - 11.9*x10*x5 - 6.9 *x10*x6 - 6*x10*x7 - 8.9*x10*x8 - 5.8*x10*x9 - 11.9*x10*x10) + objvar =E= 0; * set non default bounds * set non default levels * set non default marginals Model m / all /; m.limrow=0; m.limcol=0; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' Solve m using NLP minimizing objvar;