st_fp7e.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, and Sahinidis, N, A finite algorithm for global minimization of separable concave programs. Journal of Global Optimization 12 (1998), 1--36.
- 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:
<![CDATA[
* NLP written by GAMS Convert at 08/30/02 10:43:01
*
* 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
* 21 21 0 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 185 165 20 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,x19,x20;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;
e1.. - 3*x1 + 7*x2 - 5*x4 + x5 + x6 + 2*x8 - x9 - x10 - 9*x11 + 3*x12 + 5*x13
+ x16 + 7*x17 - 7*x18 - 4*x19 - 6*x20 =L= -5;
e2.. 7*x1 - 5*x3 + x4 + x5 + 2*x7 - x8 - x9 - 9*x10 + 3*x11 + 5*x12 + x15
+ 7*x16 - 7*x17 - 4*x18 - 6*x19 - 3*x20 =L= 2;
e3.. - 5*x2 + x3 + x4 + 2*x6 - x7 - x8 - 9*x9 + 3*x10 + 5*x11 + x14 + 7*x15
- 7*x16 - 4*x17 - 6*x18 - 3*x19 + 7*x20 =L= -1;
e4.. - 5*x1 + x2 + x3 + 2*x5 - x6 - x7 - 9*x8 + 3*x9 + 5*x10 + x13 + 7*x14
- 7*x15 - 4*x16 - 6*x17 - 3*x18 + 7*x19 =L= -3;
e5.. x1 + x2 + 2*x4 - x5 - x6 - 9*x7 + 3*x8 + 5*x9 + x12 + 7*x13 - 7*x14
- 4*x15 - 6*x16 - 3*x17 + 7*x18 - 5*x20 =L= 5;
e6.. x1 + 2*x3 - x4 - x5 - 9*x6 + 3*x7 + 5*x8 + x11 + 7*x12 - 7*x13 - 4*x14
- 6*x15 - 3*x16 + 7*x17 - 5*x19 + x20 =L= 4;
e7.. 2*x2 - x3 - x4 - 9*x5 + 3*x6 + 5*x7 + x10 + 7*x11 - 7*x12 - 4*x13
- 6*x14 - 3*x15 + 7*x16 - 5*x18 + x19 + x20 =L= -1;
e8.. 2*x1 - x2 - x3 - 9*x4 + 3*x5 + 5*x6 + x9 + 7*x10 - 7*x11 - 4*x12
- 6*x13 - 3*x14 + 7*x15 - 5*x17 + x18 + x19 =L= 0;
e9.. - x1 - x2 - 9*x3 + 3*x4 + 5*x5 + x8 + 7*x9 - 7*x10 - 4*x11 - 6*x12
- 3*x13 + 7*x14 - 5*x16 + x17 + x18 + 2*x20 =L= 9;
e10.. x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13
+ x14 + x15 + x16 + x17 + x18 + x19 + x20 =L= 40;
e11.. - (2*x1 - 0.5*sqr(x1) - sqr(x2) + 4*x2 - 1.5*sqr(x3) + 6*x3 - 2*sqr(x4)
+ 8*x4 - 2.5*sqr(x5) + 10*x5 - 3*sqr(x6) + 12*x6 - 3.5*sqr(x7) + 14*x7
- 4*sqr(x8) + 16*x8 - 4.5*sqr(x9) + 18*x9 - 5*sqr(x10) + 20*x10 - 5.5*
sqr(x11) + 22*x11 - 6*sqr(x12) + 24*x12 - 6.5*sqr(x13) + 26*x13 - 7*sqr(
x14) + 28*x14 - 7.5*sqr(x15) + 30*x15 - 8*sqr(x16) + 32*x16 - 8.5*sqr(x17
) + 34*x17 - 9*sqr(x18) + 36*x18 - 9.5*sqr(x19) + 38*x19 - 10*sqr(x20) +
40*x20) + 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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