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Instance ex14_2_7
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -0.00000000 (ANTIGONE) -0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (SCIP) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. |
| Sourceⓘ | Test Problem ex14.2.7 of Chapter 14 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 6 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 5 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 9 |
| #Linear Constraintsⓘ | 1 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 8 |
| Operands in Gen. Nonlin. Functionsⓘ | div log |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 52 |
| #Nonlinear Nonzeros in Jacobianⓘ | 40 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 17 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 5 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.2811e-02 |
| Maximal coefficientⓘ | 3.8040e+03 |
| Infeasibility of initial pointⓘ | 0.001152 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 10 2 0 8 0 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
*
* 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;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc