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## synthes2.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 synthes2.mod from MacMINLP

Point: p1
Best known point (p1): Solution value 73.04 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:41:30 * * Equation counts * Total E G L N X * 15 2 0 13 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 12 7 5 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 49 41 8 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,b7,b8,b9,b10,b11,objvar; Positive Variables x1,x2,x3,x4,x5,x6; Binary Variables b7,b8,b9,b10,b11; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15; e1.. - log(1 + x4 + x5) =L= 0; e2.. exp(x1) - 10*b7 =L= 1; e3.. exp(0.833333*x2) - 10*b8 =L= 1; e4.. 1.25*x3 - 10*b9 =L= 0; e5.. x4 + x5 - 10*b10 =L= 0; e6.. - 2*x3 + 2*x6 - 10*b11 =L= 0; e7.. - x1 - x2 - 2*x3 + x4 + 2*x6 =L= 0; e8.. - x1 - x2 - 0.75*x3 + x4 + 2*x6 =L= 0; e9.. x3 - x6 =L= 0; e10.. 2*x3 - x4 - 2*x6 =L= 0; e11.. - 0.5*x4 + x5 =L= 0; e12.. - 0.2*x4 - x5 =L= 0; e13.. b7 + b8 =E= 1; e14.. b10 + b11 =L= 1; e15.. - (exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 60*log(1 + x4 + x5) + 15 *x4 + 5*x5) + 15*x3 + 20*x6 - 5*b7 - 8*b8 - 6*b9 - 10*b10 - 6*b11 + objvar =E= 140; * set non default bounds x1.up = 2; x2.up = 2; x3.up = 2; x6.up = 3; \$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;