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## 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)

\$offlisting * 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;