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Instance ex14_2_6
| 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 ex14.2.6 of Chapter 14 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 5 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 4 |
| #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ⓘ | 7 |
| #Linear Constraintsⓘ | 1 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 6 |
| Operands in Gen. Nonlin. Functionsⓘ | div log |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 33 |
| #Nonlinear Nonzeros in Jacobianⓘ | 24 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 10 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 4 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0794e-03 |
| Maximal coefficientⓘ | 3.8164e+03 |
| Infeasibility of initial pointⓘ | 0.000554 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 8 2 0 6 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 6 6 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 35 11 24 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,objvar,x6;
Positive Variables x6;
Equations e1,e2,e3,e4,e5,e6,e7,e8;
e1.. objvar - x6 =E= 0;
e2.. 8.85*log(2.11*x1 + 3.19*x2 + 0.92*x3) - 9.85*log(1.97*x1 + 2.4*x2 + 1.4*x3
) - (3.7136*x2 - 0.865100000000001*x1 - 4.8952*x3)/(2.11*x1 + 3.19*x2 +
0.92*x3) - 0.92*log(0.92*x1 + 0.120222883700913*x2 + 0.31896673275906*x3)
+ 0.92*log(0.92*x1 + 2.4*x2 + x3) - 0.92*(0.92*x1/(0.92*x1 +
0.120222883700913*x2 + 0.31896673275906*x3) + 3.53361528312402*x2/(
1.35455252519754*x1 + 2.4*x2 + 0.707809655896681*x3) + 1.21383720135623*x3
/(1.11673022524774*x1 + 0.00499065620537111*x2 + x3)) - 3803.98/(231.47 +
x4) - x6 =L= -12.8590236275375;
e3.. 11*log(2.11*x1 + 3.19*x2 + 0.92*x3) - 12*log(1.97*x1 + 2.4*x2 + 1.4*x3) -
(5.6144*x2 - 1.3079*x1 - 7.4008*x3)/(2.11*x1 + 3.19*x2 + 0.92*x3) - 2.4*
log(1.35455252519754*x1 + 2.4*x2 + 0.707809655896681*x3) + 2.4*log(0.92*x1
+ 2.4*x2 + x3) - 2.4*(0.0460854387520165*x1/(0.92*x1 + 0.120222883700913*
x2 + 0.31896673275906*x3) + 2.4*x2/(1.35455252519754*x1 + 2.4*x2 +
0.707809655896681*x3) + 0.0020794400855713*x3/(1.11673022524774*x1 +
0.00499065620537111*x2 + x3)) - 2788.51/(220.79 + x4) - x6
=L= -11.1728763302021;
e4.. 6*log(2.11*x1 + 3.19*x2 + 0.92*x3) - 7*log(1.97*x1 + 2.4*x2 + 1.4*x3) - (
1.6192*x2 - 0.3772*x1 - 2.1344*x3)/(2.11*x1 + 3.19*x2 + 0.92*x3) - log(
1.11673022524774*x1 + 0.00499065620537111*x2 + x3) + log(0.92*x1 + 2.4*x2
+ x3) - (0.293449394138336*x1/(0.92*x1 + 0.120222883700913*x2 +
0.31896673275906*x3) + 1.69874317415203*x2/(1.35455252519754*x1 + 2.4*x2
+ 0.707809655896681*x3) + x3/(1.11673022524774*x1 + 0.00499065620537111*
x2 + x3)) - 3816.44/(227.02 + x4) - x6 =L= -13.2058768767024;
e5.. 9.85*log(1.97*x1 + 2.4*x2 + 1.4*x3) - 8.85*log(2.11*x1 + 3.19*x2 + 0.92*x3
) + (3.7136*x2 - 0.865100000000001*x1 - 4.8952*x3)/(2.11*x1 + 3.19*x2 +
0.92*x3) + 0.92*log(0.92*x1 + 0.120222883700913*x2 + 0.31896673275906*x3)
- 0.92*log(0.92*x1 + 2.4*x2 + x3) + 0.92*(0.92*x1/(0.92*x1 +
0.120222883700913*x2 + 0.31896673275906*x3) + 3.53361528312402*x2/(
1.35455252519754*x1 + 2.4*x2 + 0.707809655896681*x3) + 1.21383720135623*x3
/(1.11673022524774*x1 + 0.00499065620537111*x2 + x3)) + 3803.98/(231.47 +
x4) - x6 =L= 12.8590236275375;
e6.. 12*log(1.97*x1 + 2.4*x2 + 1.4*x3) - 11*log(2.11*x1 + 3.19*x2 + 0.92*x3) +
(5.6144*x2 - 1.3079*x1 - 7.4008*x3)/(2.11*x1 + 3.19*x2 + 0.92*x3) + 2.4*
log(1.35455252519754*x1 + 2.4*x2 + 0.707809655896681*x3) - 2.4*log(0.92*x1
+ 2.4*x2 + x3) + 2.4*(0.0460854387520165*x1/(0.92*x1 + 0.120222883700913*
x2 + 0.31896673275906*x3) + 2.4*x2/(1.35455252519754*x1 + 2.4*x2 +
0.707809655896681*x3) + 0.0020794400855713*x3/(1.11673022524774*x1 +
0.00499065620537111*x2 + x3)) + 2788.51/(220.79 + x4) - x6
=L= 11.1728763302021;
e7.. 7*log(1.97*x1 + 2.4*x2 + 1.4*x3) - 6*log(2.11*x1 + 3.19*x2 + 0.92*x3) + (
1.6192*x2 - 0.3772*x1 - 2.1344*x3)/(2.11*x1 + 3.19*x2 + 0.92*x3) + log(
1.11673022524774*x1 + 0.00499065620537111*x2 + x3) - log(0.92*x1 + 2.4*x2
+ x3) + 0.293449394138336*x1/(0.92*x1 + 0.120222883700913*x2 +
0.31896673275906*x3) + 1.69874317415203*x2/(1.35455252519754*x1 + 2.4*x2
+ 0.707809655896681*x3) + x3/(1.11673022524774*x1 + 0.00499065620537111*
x2 + x3) + 3816.44/(227.02 + x4) - x6 =L= 13.2058768767024;
e8.. x1 + x2 + x3 =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 = 40; x4.up = 90;
* set non-default levels
x1.l = 0.013;
x2.l = 0.604;
x3.l = 0.383;
x4.l = 61.583;
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