ex1223.gms:
References:
- Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
- Yuan, X, Zhang, S, and Pibouleau, L, A Mixed-Integer Nonlinear-Programming Method for Process Design. RAIRO - Recherche Operationnelle-Operations Research 22 (1988), 331-346.
- Original source: MINLP Model of Chapter 12 ex12.2.3.gms from Floudas e.a. Test Problems
Point:
p1
Best known point (p1): Solution value 4.58 (global optimum, BARON certificate)
<![CDATA[
* MINLP written by GAMS Convert at 04/17/01 16:37:46
*
* Equation counts
* Total E G L N X
* 14 5 0 9 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 12 8 4 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 40 23 17 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,b8,b9,b10,b11,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7;
Binary Variables b8,b9,b10,b11;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14;
e1.. x1 + x2 + x3 + b8 + b9 + b10 =L= 5;
e2.. sqr(x6) + sqr(x1) + sqr(x2) + sqr(x3) =L= 5.5;
e3.. x1 + b8 =L= 1.2;
e4.. x2 + b9 =L= 1.8;
e5.. x3 + b10 =L= 2.5;
e6.. x1 + b11 =L= 1.2;
e7.. sqr(x5) + sqr(x2) =L= 1.64;
e8.. sqr(x6) + sqr(x3) =L= 4.25;
e9.. sqr(x5) + sqr(x3) =L= 4.64;
e10.. x4 - b8 =E= 0;
e11.. x5 - b9 =E= 0;
e12.. x6 - b10 =E= 0;
e13.. x7 - b11 =E= 0;
e14.. - (sqr(x4 - 1) + sqr(x5 - 2) + sqr(x6 - 1) - log(1 + x7) + sqr(x1 - 1)
+ sqr(x2 - 2) + sqr(x3 - 3)) + objvar =E= 0;
* set non default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
$if set nostart $goto modeldef
* set non default levels
* set non default marginals
$label modeldef
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
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