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## synthes1.gms:

#### References:

• Leyffer, S, MacMINLP: AMPL Collection of Mixed Integer Nonlinear Programs.
• Floudas, C A, and Schweiger, C A, MINOPT Model Library.
• Duran, M A, and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-Integer Nonlinear Programs. Mathematical Programming 36 (1986), 307-339.
• Original source: AMPL model synthes1.mod from MacMINLP

Point: p1
Best known point (p1): Solution value 6.01 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:41:28 * * Equation counts * Total E G L N X * 7 1 2 4 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 7 4 3 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 23 17 6 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,b4,b5,b6,objvar; Positive Variables x1,x2,x3; Binary Variables b4,b5,b6; Equations e1,e2,e3,e4,e5,e6,e7; e1.. - (-18*log(1 + x2) - 19.2*log(1 + x1 - x2) + 10*x1) + 7*x3 - 5*b4 - 6*b5 - 8*b6 + objvar =E= 10; e2.. 0.8*log(1 + x2) + 0.96*log(1 + x1 - x2) - 0.8*x3 =G= 0; e3.. log(1 + x2) + 1.2*log(1 + x1 - x2) - x3 - 2*b6 =G= -2; e4.. - x1 + x2 =L= 0; e5.. x2 - 2*b4 =L= 0; e6.. x1 - x2 - 2*b5 =L= 0; e7.. b4 + b5 =L= 1; * set non default bounds x1.up = 2; x2.up = 2; x3.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;