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## st_test4.gms:

#### References:

• Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
• Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, 1999. PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne

Point: p1
Best known point (p1): Solution value -7.00 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 09/01/02 10:53:46 * * Equation counts * Total E G L N X C * 6 1 0 5 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 7 1 0 6 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 37 35 2 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,i5,i6,objvar; Integer Variables i1,i2,i3,i4,i5,i6; Equations e1,e2,e3,e4,e5,e6; e1.. i1 + 2*i2 + 8*i3 + i4 + 3*i5 + 5*i6 =L= 16; e2.. - 8*i1 - 4*i2 - 2*i3 + 2*i4 + 4*i5 - i6 =L= -1; e3.. 2*i1 + 0.5*i2 + 0.2*i3 - 3*i4 - i5 - 4*i6 =L= 24; e4.. 0.2*i1 + 2*i2 + 0.1*i3 - 4*i4 + 2*i5 + 2*i6 =L= 12; e5.. - 0.1*i1 - 0.5*i2 + 2*i3 + 5*i4 - 5*i5 + 3*i6 =L= 3; e6.. - (0.5*i1*i1 + 6.5*i1 + 7*i6*i6 - i6) + i2 + 2*i3 - 3*i4 + 2*i5 + objvar =E= 0; * set non default bounds i1.up = 1E15; i2.up = 1E15; i3.up = 1E15; i4.up = 1; i5.up = 1; i6.up = 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;