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## ex1223a.gms:

#### References:

• GAMS Development, Reformulation of Models from Handbook of Test Problems in Local and Global Optimization.
• 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 16:37:48 * * Equation counts * Total E G L N X * 10 1 0 9 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 8 4 4 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 32 23 9 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,b4,b5,b6,b7,objvar; Positive Variables x1,x2,x3; Binary Variables b4,b5,b6,b7; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10; e1.. x1 + x2 + x3 + b4 + b5 + b6 =L= 5; e2.. sqr(x1) + sqr(x2) + sqr(x3) + b6 =L= 5.5; e3.. x1 + b4 =L= 1.2; e4.. x2 + b5 =L= 1.8; e5.. x3 + b6 =L= 2.5; e6.. x1 + b7 =L= 1.2; e7.. sqr(x2) + b5 =L= 1.64; e8.. sqr(x3) + b6 =L= 4.25; e9.. sqr(x3) + b5 =L= 4.64; e10.. - (sqr(x1 - 1) + sqr(x2 - 2) + sqr(x3 - 3)) + b4 + 3*b5 + b6 + 0.693147180559945*b7 + objvar =E= 6; * set non default bounds x1.up = 10; x2.up = 10; x3.up = 10; \$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;