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## nvs20.gms:

#### References:

• Tawarmalani, M, and Sahinidis, N, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, P M, and Romeijn, E, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches. Kluwer Academic Publishers, 2001.
• Gupta, O K, and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming. Management Science 13 (1985), 1533-1546.

Point: p1
Best known point (p1): Solution value 230.92 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:19 * * Equation counts * Total E G L N X C * 9 1 8 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 17 12 0 5 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 70 54 16 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,i5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,objvar; Positive Variables x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; Integer Variables i1,i2,i3,i4,i5; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9; e1.. 0.22*i1 + 0.2*i2 + 0.19*i3 + 0.25*i4 + 0.15*i5 + 0.11*x6 + 0.12*x7 + 0.13*x8 + x9 =G= 2.5; e2.. - 1.46*i1 - 1.3*i3 + 1.82*i4 - 1.15*i5 + 0.8*x7 + x10 =G= 1.1; e3.. 1.29*i1 - 0.89*i2 - 1.16*i5 - 0.96*x6 - 0.49*x8 + x11 =G= -3.1; e4.. - 1.1*i1 - 1.06*i2 + 0.95*i3 - 0.54*i4 - 1.78*x6 - 0.41*x7 + x12 =G= -3.5; e5.. - 1.43*i4 + 1.51*i5 + 0.59*x6 - 0.33*x7 - 0.43*x8 + x13 =G= 1.3; e6.. - 1.72*i2 - 0.33*i3 + 1.62*i5 + 1.24*x6 + 0.21*x7 - 0.26*x8 + x14 =G= 2.1; e7.. 1.12*i1 + 0.31*i4 + 1.12*x7 - 0.36*x9 + x15 =G= 2.3; e8.. 0.45*i2 + 0.26*i3 - 1.1*i4 + 0.58*i5 - 1.03*x7 + 0.1*x8 + x16 =G= -1.5; e9.. - (sqr(1 + sqr(i1) + i1) + (1 + sqr(i1) + i1)*(1 + sqr(i4) + i4) + (1 + sqr(i1) + i1)*(1 + sqr(x7) + x7) + (1 + sqr(i1) + i1)*(1 + sqr(x8) + x8) + (1 + sqr(i1) + i1)*(1 + sqr(x16) + x16) + sqr(1 + sqr(i2) + i2) + (1 + sqr(i2) + i2)*(1 + sqr(i3) + i3) + (1 + sqr(i2) + i2)*(1 + sqr(x7) + x7) + (1 + sqr(i2) + i2)*(1 + sqr(x10) + x10) + sqr(1 + sqr(i3) + i3) + (1 + sqr(i3) + i3)*(1 + sqr(x7) + x7) + (1 + sqr(i3) + i3)*(1 + sqr(x9) + x9) + (1 + sqr(i3) + i3)*(1 + sqr(x10) + x10) + (1 + sqr(i3) + i3)*(1 + sqr( x14) + x14) + sqr(1 + sqr(i4) + i4) + (1 + sqr(i4) + i4)*(1 + sqr(x7) + x7 ) + (1 + sqr(i4) + i4)*(1 + sqr(x11) + x11) + (1 + sqr(i4) + i4)*(1 + sqr( x15) + x15) + sqr(1 + sqr(i5) + i5) + (1 + sqr(i5) + i5)*(1 + sqr(x6) + x6 ) + (1 + sqr(i5) + i5)*(1 + sqr(x10) + x10) + (1 + sqr(i5) + i5)*(1 + sqr( x12) + x12) + (1 + sqr(i5) + i5)*(1 + sqr(x16) + x16) + sqr(1 + sqr(x6) + x6) + (1 + sqr(x6) + x6)*(1 + sqr(x8) + x8) + (1 + sqr(x6) + x6)*(1 + sqr( x15) + x15) + sqr(1 + sqr(x7) + x7) + (1 + sqr(x7) + x7)*(1 + sqr(x11) + x11) + (1 + sqr(x7) + x7)*(1 + sqr(x13) + x13) + sqr(1 + sqr(x8) + x8) + ( 1 + sqr(x8) + x8)*(1 + sqr(x10) + x10) + (1 + sqr(x8) + x8)*(1 + sqr(x15) + x15) + sqr(1 + sqr(x9) + x9) + (1 + sqr(x9) + x9)*(1 + sqr(x12) + x12) + (1 + sqr(x9) + x9)*(1 + sqr(x16) + x16) + sqr(1 + sqr(x10) + x10) + (1 + sqr(x10) + x10)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x11) + x11) + (1 + sqr(x11) + x11)*(1 + sqr(x13) + x13) + sqr(1 + sqr(x12) + x12) + (1 + sqr( x12) + x12)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x13) + x13) + (1 + sqr(x13) + x13)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x14) + x14) + sqr(1 + sqr(x15) + x15) + sqr(1 + sqr(x16) + x16)) + objvar =E= 0; * set non default bounds i1.up = 200; i2.up = 200; i3.up = 200; i4.up = 200; i5.up = 200; x6.up = 200; x7.up = 200; x8.up = 200; x9.up = 200; x10.up = 200; x11.up = 200; x12.up = 200; x13.up = 200; x14.up = 200; x15.up = 200; x16.up = 200; \$if set nostart \$goto modeldef * set non default levels i1.l = 1; i2.l = 1; i3.l = 1; i4.l = 1; i5.l = 1; x6.l = 1; x7.l = 1; x8.l = 1; x9.l = 1; x10.l = 1; x11.l = 1; x12.l = 1; x13.l = 1; x14.l = 1; x15.l = 1; x16.l = 1; * 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;