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## meanvarxsc.gms:

#### References:

• GAMS Development, Reformulation of Models from GAMS Library.
• Dahl, H, Meeraus, A, and Zenios, S A, Some Financial Optimization Models: Risk Management. In Zenios, S A, Ed, Financial Optimization. Cambridge University Press, New York, NY, 1993.
• Original source: GAMS model meanvarx.gms from Gams Model Library

Point: p1
Best known point (p1): Solution value 14.37 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:38:59 * * Equation counts * Total E G L N X * 31 9 0 22 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 36 8 14 0 0 0 14 0 * FX 2 0 0 0 0 0 2 0 * * Nonzero counts * Total const NL DLL * 83 76 7 0 * * Solve m using MINLP minimizing objvar; Variables objvar,x2,x3,x4,x5,x6,x7,x8,sc9,sc10,sc11,sc12,sc13,sc14,sc15,sc16 ,sc17,sc18,sc19,sc20,sc21,sc22,b23,b24,b25,b26,b27,b28,b29,b30,b31 ,b32,b33,b34,b35,b36; Positive Variables x2,x3,x4,x5,x6,x7,x8; Binary Variables b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36; Semicont Variables sc9,sc10,sc11,sc12,sc13,sc14,sc15,sc16,sc17,sc18,sc19,sc20 ,sc21,sc22; 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,e25,e26,e27,e28,e29,e30,e31; e1.. x2 + x3 + x4 + x5 + x6 + x7 + x8 =E= 1; e2.. x2 - sc9 + sc16 =E= 0.2; e3.. x3 - sc10 + sc17 =E= 0.2; e4.. x4 - sc11 + sc18 =E= 0; e5.. x5 - sc12 + sc19 =E= 0; e6.. x6 - sc13 + sc20 =E= 0.2; e7.. x7 - sc14 + sc21 =E= 0.2; e8.. x8 - sc15 + sc22 =E= 0.2; e9.. sc9 + sc10 + sc11 + sc12 + sc13 + sc14 + sc15 =L= 0.3; e10.. sc9 - 0.11*b23 =L= 0; e11.. sc10 - 0.1*b24 =L= 0; e12.. sc11 - 0.07*b25 =L= 0; e13.. sc12 - 0.11*b26 =L= 0; e14.. sc13 - 0.2*b27 =L= 0; e15.. sc14 - 0.1*b28 =L= 0; e16.. sc15 - 0.1*b29 =L= 0; e17.. sc16 - 0.2*b30 =L= 0; e18.. sc17 - 0.15*b31 =L= 0; e19.. sc18 =L= 0; e20.. sc19 =L= 0; e21.. sc20 - 0.1*b34 =L= 0; e22.. sc21 - 0.15*b35 =L= 0; e23.. sc22 - 0.2*b36 =L= 0; e24.. b23 + b30 =L= 1; e25.. b24 + b31 =L= 1; e26.. b25 + b32 =L= 1; e27.. b26 + b33 =L= 1; e28.. b27 + b34 =L= 1; e29.. b28 + b35 =L= 1; e30.. b29 + b36 =L= 1; e31.. - (42.18*x2*x2 + 40.36*x2*x3 + 21.76*x2*x4 + 10.6*x2*x5 + 24.64*x2*x6 + 47.68*x2*x7 + 34.82*x2*x8 + 70.89*x3*x3 + 43.16*x3*x4 + 30.82*x3*x5 + 46.48*x3*x6 + 47.6*x3*x7 + 25.24*x3*x8 + 25.51*x4*x4 + 19.2*x4*x5 + 45.26 *x4*x6 + 26.44*x4*x7 + 9.4*x4*x8 + 22.33*x5*x5 + 20.64*x5*x6 + 20.92*x5* x7 + 2*x5*x8 + 30.01*x6*x6 + 32.72*x6*x7 + 14.4*x6*x8 + 42.23*x7*x7 + 19.8*x7*x8 + 16.42*x8*x8 - 0.06435*x2 - 0.0548*x3 - 0.02505*x4 - 0.0762* x5 - 0.03815*x6 - 0.0927*x7 - 0.031*x8) + objvar =E= 0; * set non default bounds sc9.lo = 0.03; sc9.up = 0.11; sc10.lo = 0.04; sc10.up = 0.1; sc11.lo = 0.04; sc11.up = 0.07; sc12.lo = 0.03; sc12.up = 0.11; sc13.lo = 0.03; sc13.up = 0.2; sc14.lo = 0.03; sc14.up = 0.1; sc15.lo = 0.03; sc15.up = 0.1; sc16.lo = 0.02; sc16.up = 0.2; sc17.lo = 0.02; sc17.up = 0.15; sc18.fx = 0; sc19.fx = 0; sc20.lo = 0.04; sc20.up = 0.1; sc21.lo = 0.04; sc21.up = 0.15; sc22.lo = 0.04; sc22.up = 0.2; \$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;