st_qpc-m4.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:
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* NLP written by GAMS Convert at 08/31/02 19:18:14
*
* 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 - 0.06*x1*x1 - 0.047*x1*x2 + 10*x2 - 0.047*x1*x3 + 10*x3 + 0.01
*x1*x4 + 10*x4 - 0.01*x1*x5 + 10*x5 - 0.018*x1*x6 + 10*x6 - 0.026*x1*x7
+ 10*x7 + 0.018*x1*x8 + 10*x8 - 0.05*x1*x10 + 10*x10 - 0.047*x2*x1 -
0.11*x2*x2 - 0.024*x2*x3 + 0.025*x2*x4 - 0.038*x2*x5 - 0.05*x2*x6 - 0.05*
x2*x7 - 0.017*x2*x8 + 0.005*x2*x9 + 10*x9 - 0.039*x2*x10 - 0.047*x3*x1 -
0.024*x3*x2 - 0.11*x3*x3 + 0.009*x3*x4 - 0.026*x3*x5 - 0.034*x3*x6 -
0.066*x3*x7 + 0.014*x3*x8 - 0.005*x3*x9 - 0.085*x3*x10 + 0.01*x4*x1 +
0.025*x4*x2 + 0.009*x4*x3 - 0.068*x4*x4 + 0.023*x4*x5 + 0.011*x4*x6 +
0.014*x4*x7 - 0.017*x4*x8 - 0.077*x4*x9 - 0.017*x4*x10 - 0.01*x5*x1 -
0.038*x5*x2 - 0.026*x5*x3 + 0.023*x5*x4 - 0.12*x5*x5 - 0.083*x5*x6 -
0.022*x5*x7 - 0.017*x5*x8 + 0.003*x5*x9 + 0.034*x5*x10 - 0.018*x6*x1 -
0.05*x6*x2 - 0.034*x6*x3 + 0.011*x6*x4 - 0.083*x6*x5 - 0.115*x6*x6 -
0.051*x6*x7 - 0.015*x6*x8 - 0.022*x6*x9 + 0.012*x6*x10 - 0.026*x7*x1 -
0.05*x7*x2 - 0.066*x7*x3 + 0.014*x7*x4 - 0.022*x7*x5 - 0.051*x7*x6 -
0.157*x7*x7 - 0.012*x7*x8 - 0.019*x7*x9 - 0.057*x7*x10 + 0.018*x8*x1 -
0.017*x8*x2 + 0.014*x8*x3 - 0.017*x8*x4 - 0.017*x8*x5 - 0.015*x8*x6 -
0.012*x8*x7 - 0.033*x8*x8 - 0.022*x8*x9 + 0.006*x8*x10 + 0.005*x9*x2 -
0.005*x9*x3 - 0.077*x9*x4 + 0.003*x9*x5 - 0.022*x9*x6 - 0.019*x9*x7 -
0.022*x9*x8 - 0.11*x9*x9 - 0.009*x9*x10 - 0.05*x10*x1 - 0.039*x10*x2 -
0.085*x10*x3 - 0.017*x10*x4 + 0.034*x10*x5 + 0.012*x10*x6 - 0.057*x10*x7
+ 0.006*x10*x8 - 0.009*x10*x9 - 0.226*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;
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