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## st_testph4.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 -80.50 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 09/01/02 11:08:02 * * Equation counts * Total E G L N X C * 11 1 0 10 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 4 1 0 3 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 28 25 3 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,objvar; Integer Variables i1,i2,i3; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11; e1.. i1 =L= 4; e2.. i2 =L= 4; e3.. i3 =L= 4; e4.. 2*i1 + 3*i2 + 4*i3 =L= 35; e5.. 2*i1 + 3*i2 - 4*i3 =L= 19; e6.. 2*i1 - 3*i2 + 4*i3 =L= 23; e7.. - 2*i1 + 3*i2 + 4*i3 =L= 27; e8.. 2*i1 - 3*i2 - 4*i3 =L= 7; e9.. - 2*i1 - 3*i2 + 4*i3 =L= 15; e10.. - 2*i1 + 3*i2 - 4*i3 =L= 11; e11.. - (3.5*i1*i1 - 35*i1 + 0.5*i2*i2 + 3*i2 + 2*i3*i3 + 4*i3) + objvar =E= 0; * set non default bounds i1.up = 100; i2.up = 100; i3.up = 100; \$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;