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## st_e21.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.
• Stephanopoulos, G, and Westerberg, A W, The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization. Journal of Optimization Theory and Applications 15 (1975), 285-309.

Point:

* NLP written by GAMS Convert at 08/29/02 12:49:53 * * Equation counts * Total E G L N X C * 7 4 0 3 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 7 7 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 21 18 3 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,objvar; Positive Variables x1,x2,x3,x4,x5,x6; Equations e1,e2,e3,e4,e5,e6,e7; e1.. - 3*x1 + x2 - 3*x4 =E= 0; e2.. - 2*x2 + x3 - 2*x5 =E= 0; e3.. 4*x4 - x6 =E= 0; e4.. x1 + 2*x4 =L= 4; e5.. x2 + x5 =L= 4; e6.. x3 + x6 =L= 6; e7.. - (x1**0.6 + x2**0.6 + x3**0.4 - 4*x3) - 2*x4 - 5*x5 + x6 + objvar =E= 0; * set non default bounds x1.up = 3; x2.up = 4; x3.up = 4; x4.up = 2; x5.up = 2; x6.up = 6; * set non default levels * 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;