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## synthes3.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 synthes3.mod from MacMINLP

Point: p1
Best known point (p1): Solution value 68.01 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:41:31 * * Equation counts * Total E G L N X * 24 3 0 21 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 18 10 8 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 91 79 12 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,b10,b11,b12,b13,b14,b15,b16,b17,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9; Binary Variables b10,b11,b12,b13,b14,b15,b16,b17; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19 ,e20,e21,e22,e23,e24; e1.. (-1.5*log(1 + x5)) - log(1 + x6) - x8 =L= 0; e2.. - log(1 + x3 + x4) =L= 0; e3.. - x1 - x2 + x3 + 2*x4 + 0.8*x5 + 0.8*x6 - 0.5*x7 - x8 - 2*x9 =L= 0; e4.. - x1 - x2 + 2*x4 + 0.8*x5 + 0.8*x6 - 2*x7 - x8 - 2*x9 =L= 0; e5.. - 2*x4 - 0.8*x5 - 0.8*x6 + 2*x7 + x8 + 2*x9 =L= 0; e6.. - 0.8*x5 - 0.8*x6 + x8 =L= 0; e7.. - x4 + x7 + x9 =L= 0; e8.. - 0.4*x5 - 0.4*x6 + 1.5*x8 =L= 0; e9.. 0.16*x5 + 0.16*x6 - 1.2*x8 =L= 0; e10.. x3 - 0.8*x4 =L= 0; e11.. - x3 + 0.4*x4 =L= 0; e12.. exp(x1) - 10*b10 =L= 1; e13.. exp(0.833333*x2) - 10*b11 =L= 1; e14.. x7 - 10*b12 =L= 0; e15.. 0.8*x5 + 0.8*x6 - 10*b13 =L= 0; e16.. 2*x4 - 2*x7 - 2*x9 - 10*b14 =L= 0; e17.. x5 - 10*b15 =L= 0; e18.. x6 - 10*b16 =L= 0; e19.. x3 + x4 - 10*b17 =L= 0; e20.. b10 + b11 =E= 1; e21.. b13 + b14 =L= 1; e22.. - b13 + b15 + b16 =E= 0; e23.. b12 - b17 =L= 0; e24.. - (exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 65*log(1 + x3 + x4) + 15 *x3 + 80*x4 - 90*log(1 + x5) + 25*x5 - 80*log(1 + x6) + 35*x6) + 40*x7 - 15*x8 + 35*x9 - 5*b10 - 8*b11 - 6*b12 - 10*b13 - 6*b14 - 7*b15 - 4*b16 - 5*b17 + objvar =E= 120; * set non default bounds x1.up = 2; x2.up = 2; x3.up = 1; x4.up = 2; x5.up = 2; x6.up = 2; x7.up = 2; x8.up = 1; x9.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;