ex14_2_7.gms

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ex14_2_7.gms:

Reference:

Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
Original source: Global Model of Chapter 14 ex14.2.7.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value 0.0000

* NLP written by GAMS Convert at 07/19/01 13:40:30 * * Equation counts * Total E G L N X * 10 2 0 8 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 * 54 14 40 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,objvar,x7; Positive Variables x7; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10; e1.. objvar - x7 =E= 0; e2.. 8.85*log(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 9.85*log(1.97*x1 + 3.01* x2 + 2.4*x3 + 3.86*x4) - (3.8613*x2 - 0.865100000000001*x1 + 3.7136*x3 - 0.632999999999999*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 0.92*log( 0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481* x4) + 0.92*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 0.92*(0.92*x1/(0.92 *x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 5.42978509857797*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291* x3 + 1.70144966342223*x4) + 3.53361528312402*x3/(1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 5.92791255201582*x4/ (1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4) ) - 3803.98/(231.47 + x5) - x7 =L= -12.8590236275375; e3.. 14.05*log(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 15.05*log(1.97*x1 + 3.01 *x2 + 2.4*x3 + 3.86*x4) - (7.26510000000001*x2 - 1.6277*x1 + 6.9872*x3 - 1.191*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 3.01*log( 1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 3.01*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 3.01*( 0.0228107346172588*x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913* x3 + 0.161199992780481*x4) + 3.01*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 1.48314676153655*x3/( 1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 7.51049429784342*x4/(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) - 2735.58621973158/(226.276 + x5) - x7 =L= -11.2296864040814; e4.. 11*log(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 12*log(1.97*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - (5.83770000000001*x2 - 1.3079*x1 + 5.6144*x3 - 0.956999999999998*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 2.4*log( 1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 2.4*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 2.4*(0.0460854387520165 *x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 3.66171411047386*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 2.4*x3/(1.35455252519754* x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 4.17479603222384*x4/(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) - 2788.51/(220.79 + x5) - x7 =L= -11.1728763302021; e5.. 18.3*log(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 19.3*log(1.97*x1 + 3.01* x2 + 2.4*x3 + 3.86*x4) - (8.23500000000001*x2 - 1.845*x1 + 7.92*x3 - 1.35* x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) - 3.86*log(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4) + 3.86*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 3.86*(0.0384207236678868*x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 1.32677810541474*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 1.64761511983392*x3/(1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 3.86*x4/( 1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) - 2739.24733002944/(226.28 + x5) - x7 =L= -11.3821403387577; e6.. 9.85*log(1.97*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 8.85*log(2.11*x1 + 3.97* x2 + 3.19*x3 + 4.5*x4) + (3.8613*x2 - 0.865100000000001*x1 + 3.7136*x3 - 0.632999999999999*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) + 0.92*log( 0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481* x4) - 0.92*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) + 0.92*(0.92*x1/(0.92 *x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 5.42978509857797*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291* x3 + 1.70144966342223*x4) + 3.53361528312402*x3/(1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 5.92791255201582*x4/ (1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4) ) + 3803.98/(231.47 + x5) - x7 =L= 12.8590236275375; e7.. 15.05*log(1.97*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 14.05*log(2.11*x1 + 3.97 *x2 + 3.19*x3 + 4.5*x4) + (7.26510000000001*x2 - 1.6277*x1 + 6.9872*x3 - 1.191*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) + 3.01*log( 1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) - 3.01*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) + 3.01*( 0.0228107346172588*x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913* x3 + 0.161199992780481*x4) + 3.01*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 1.48314676153655*x3/( 1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 7.51049429784342*x4/(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) + 2735.58621973158/(226.276 + x5) - x7 =L= 11.2296864040814; e8.. 12*log(1.97*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 11*log(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) + (5.83770000000001*x2 - 1.3079*x1 + 5.6144*x3 - 0.956999999999998*x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) + 2.4*log( 1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) - 2.4*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) + 2.4*(0.0460854387520165 *x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 3.66171411047386*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 2.4*x3/(1.35455252519754* x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 4.17479603222384*x4/(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) + 2788.51/(220.79 + x5) - x7 =L= 11.1728763302021; e9.. 19.3*log(1.97*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) - 18.3*log(2.11*x1 + 3.97* x2 + 3.19*x3 + 4.5*x4) + (8.23500000000001*x2 - 1.845*x1 + 7.92*x3 - 1.35* x4)/(2.11*x1 + 3.97*x2 + 3.19*x3 + 4.5*x4) + 3.86*log(1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4) - 3.86*log(0.92*x1 + 3.01*x2 + 2.4*x3 + 3.86*x4) + 3.86*(0.0384207236678868*x1/(0.92*x1 + 0.074630773041249*x2 + 0.120222883700913*x3 + 0.161199992780481*x4) + 1.32677810541474*x2/(1.65960208993081*x1 + 3.01*x2 + 2.91963915785291*x3 + 1.70144966342223*x4) + 1.64761511983392*x3/(1.35455252519754*x1 + 1.86011323009376*x2 + 2.4*x3 + 2.64991431773289*x4) + 3.86*x4/( 1.41287034918512*x1 + 5.85662897318878*x2 + 2.5957281029371*x3 + 3.86*x4)) + 2739.24733002944/(226.28 + x5) - x7 =L= 11.3821403387577; e10.. x1 + x2 + x3 + x4 =E= 1; * set non default bounds x1.lo = 1E-6; x1.up = 1; x2.lo = 1E-6; x2.up = 1; x3.lo = 1E-6; x3.up = 1; x4.lo = 1E-6; x4.up = 1; x5.lo = 40; x5.up = 90; * set non default levels x1.l = 0.322; x2.l = 0.322; x3.l = 0.222; x4.l = 0.133; x5.l = 63.558; * 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;