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## himmel16.gms:

#### Reference:

• Himmelblau, D M, Problem Number 16. In Applied Nonlinear Programming. Mc Graw Hill, New York, 1972.
• Original source: GAMS Model of himmel16.gms from GAMS Model Library

Point: p1
Best known point: p1 with value 0.8660

* NLP written by GAMS Convert at 07/30/01 17:04:27 * * Equation counts * Total E G L N X * 22 7 0 15 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 19 19 0 0 0 0 0 0 * FX 3 3 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 97 13 84 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18 ,objvar; Positive Variables x1,x7,x8; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19 ,e20,e21,e22; e1.. sqr(x1 - x2) + sqr(x7 - x8) =L= 1; e2.. sqr(x1 - x3) + sqr(x7 - x9) =L= 1; e3.. sqr(x1 - x4) + sqr(x7 - x10) =L= 1; e4.. sqr(x1 - x5) + sqr(x7 - x11) =L= 1; e5.. sqr(x1 - x6) + sqr(x7 - x12) =L= 1; e6.. sqr(x2 - x3) + sqr(x8 - x9) =L= 1; e7.. sqr(x2 - x4) + sqr(x8 - x10) =L= 1; e8.. sqr(x2 - x5) + sqr(x8 - x11) =L= 1; e9.. sqr(x2 - x6) + sqr(x8 - x12) =L= 1; e10.. sqr(x3 - x4) + sqr(x9 - x10) =L= 1; e11.. sqr(x3 - x5) + sqr(x9 - x11) =L= 1; e12.. sqr(x3 - x6) + sqr(x9 - x12) =L= 1; e13.. sqr(x4 - x5) + sqr(x10 - x11) =L= 1; e14.. sqr(x4 - x6) + sqr(x10 - x12) =L= 1; e15.. sqr(x5 - x6) + sqr(x11 - x12) =L= 1; e16.. - x13 - x14 - x15 - x16 - x17 - x18 - objvar =E= 0; e17.. - 0.5*(x1*x8 - x7*x2) + x13 =E= 0; e18.. - 0.5*(x2*x9 - x8*x3) + x14 =E= 0; e19.. - 0.5*(x3*x10 - x9*x4) + x15 =E= 0; e20.. - 0.5*(x4*x11 - x10*x5) + x16 =E= 0; e21.. - 0.5*(x5*x12 - x11*x6) + x17 =E= 0; e22.. - 0.5*(x6*x7 - x12*x1) + x18 =E= 0; * set non default bounds x1.fx = 0; x7.fx = 0; x8.fx = 0; * set non default levels x2.l = 0.5; x3.l = 0.5; x4.l = 0.5; x9.l = 0.4; x10.l = 0.8; x11.l = 0.8; x12.l = 0.4; * set non default marginals Model m / all /; m.limrow=0; m.limcol=0; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' Solve m using NLP minimizing objvar;