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## ex1226.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.
• Porn, R, Harjunkoski, I, and Westerlund, T, Convexification of Different Classes of Non-Convex MINLP Problems. Computers and Chemical Engineering 23 (1999), 439-448.
• Original source: MINLP Model of Chapter 12 ex12.2.5.gms from Floudas e.a. Test Problems

Point: p1
Best known point (p1): Solution value -17.00 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:37:55 * * Equation counts * Total E G L N X * 6 2 0 4 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 6 3 3 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 15 13 2 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,b3,b4,b5,objvar; Binary Variables b3,b4,b5; Equations e1,e2,e3,e4,e5,e6; e1.. 8*x1 - 2*x1**0.5*sqr(x2) + 11*x2 + 2*sqr(x2) - 2*x2**0.5 =L= 39; e2.. x1 - x2 =L= 3; e3.. 3*x1 + 2*x2 =L= 24; e4.. x2 - b3 - 2*b4 - 4*b5 =E= 1; e5.. b4 + b5 =L= 1; e6.. 5*x1 - 3*x2 + objvar =E= 0; * set non default bounds x1.lo = 1; x1.up = 10; x2.lo = 1; x2.up = 6; \$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;