MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance ex6_2_7
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -4.58704966 (ANTIGONE) -1.06726714 (BARON) -8.49978555 (COUENNE) -1.35473709 (GUROBI) -2.72829129 (LINDO) -1.16454153 (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. McDonald, C M and Floudas, C A, GLOPEQ: A New Computational Tool for the Phase and Chemical Equilibrium Problem, Computers and Chemical Engineering, 21:1, 1997, 1-23. |
| Sourceⓘ | Test Problem ex6.2.7 of Chapter 6 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 9 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 9 |
| #Nonlinear Nonzeros in Objectiveⓘ | 9 |
| #Constraintsⓘ | 3 |
| #Linear Constraintsⓘ | 3 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | log mul |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 9 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 27 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.9638e-02 |
| Maximal coefficientⓘ | 4.5876e+01 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 4 4 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 10 10 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 19 10 9 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10;
Equations e1,e2,e3,e4;
e1.. -(log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*(10.4807341082197*x2 +
38.5043409542885*x5 + 8.73945638067505*x8) + 0.102582206615077*x2 -
4.55292602721008*x5 + 0.0196376909050935*x8 + 0.240734108219679*log(x2)*x2
+ 2.64434095428848*log(x5)*x5 + 0.399456380675047*log(x8)*x8 -
0.240734108219679*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x2 -
2.64434095428848*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x5 -
0.399456380675047*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x8 + 11.24*log(x2
)*x2 + 36.86*log(x5)*x5 + 9.34*log(x8)*x8 - 11.24*log(2.248*x2 + 7.372*x5
+ 1.868*x8)*x2 - 36.86*log(2.248*x2 + 7.372*x5 + 1.868*x8)*x5 - 9.34*log(
2.248*x2 + 7.372*x5 + 1.868*x8)*x8 + log(2.248*x2 + 7.372*x5 + 1.868*x8)*(
2.248*x2 + 7.372*x5 + 1.868*x8) + 2.248*log(x2)*x2 + 7.372*log(x5)*x5 +
1.868*log(x8)*x8 - 2.248*log(2.248*x2 + 5.82088173817021*x5 +
0.382446861901943*x8)*x2 - 7.372*log(0.972461133672523*x2 + 7.372*x5 +
1.1893141713454*x8)*x5 - 1.868*log(1.86752460515164*x2 + 2.61699842799583*
x5 + 1.868*x8)*x8 + log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)*(
10.4807341082197*x3 + 38.5043409542885*x6 + 8.73945638067505*x9) +
0.102582206615077*x3 - 4.55292602721008*x6 + 0.0196376909050935*x9 +
0.240734108219679*log(x3)*x3 + 2.64434095428848*log(x6)*x6 +
0.399456380675047*log(x9)*x9 - 0.240734108219679*log(2.4088*x3 + 8.8495*x6
+ 2.0086*x9)*x3 - 2.64434095428848*log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)
*x6 - 0.399456380675047*log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)*x9 + 11.24*
log(x3)*x3 + 36.86*log(x6)*x6 + 9.34*log(x9)*x9 - 11.24*log(2.248*x3 +
7.372*x6 + 1.868*x9)*x3 - 36.86*log(2.248*x3 + 7.372*x6 + 1.868*x9)*x6 -
9.34*log(2.248*x3 + 7.372*x6 + 1.868*x9)*x9 + log(2.248*x3 + 7.372*x6 +
1.868*x9)*(2.248*x3 + 7.372*x6 + 1.868*x9) + 2.248*log(x3)*x3 + 7.372*log(
x6)*x6 + 1.868*log(x9)*x9 - 2.248*log(2.248*x3 + 5.82088173817021*x6 +
0.382446861901943*x9)*x3 - 7.372*log(0.972461133672523*x3 + 7.372*x6 +
1.1893141713454*x9)*x6 - 1.868*log(1.86752460515164*x3 + 2.61699842799583*
x6 + 1.868*x9)*x9 + log(2.4088*x4 + 8.8495*x7 + 2.0086*x10)*(
10.4807341082197*x4 + 38.5043409542885*x7 + 8.73945638067505*x10) +
0.102582206615077*x4 - 4.55292602721008*x7 + 0.0196376909050935*x10 +
0.240734108219679*log(x4)*x4 + 2.64434095428848*log(x7)*x7 +
0.399456380675047*log(x10)*x10 - 0.240734108219679*log(2.4088*x4 + 8.8495*
x7 + 2.0086*x10)*x4 - 2.64434095428848*log(2.4088*x4 + 8.8495*x7 + 2.0086*
x10)*x7 - 0.399456380675047*log(2.4088*x4 + 8.8495*x7 + 2.0086*x10)*x10 +
11.24*log(x4)*x4 + 36.86*log(x7)*x7 + 9.34*log(x10)*x10 - 11.24*log(2.248*
x4 + 7.372*x7 + 1.868*x10)*x4 - 36.86*log(2.248*x4 + 7.372*x7 + 1.868*x10)
*x7 - 9.34*log(2.248*x4 + 7.372*x7 + 1.868*x10)*x10 + log(2.248*x4 + 7.372
*x7 + 1.868*x10)*(2.248*x4 + 7.372*x7 + 1.868*x10) + 2.248*log(x4)*x4 +
7.372*log(x7)*x7 + 1.868*log(x10)*x10 - 2.248*log(2.248*x4 +
5.82088173817021*x7 + 0.382446861901943*x10)*x4 - 7.372*log(
0.972461133672523*x4 + 7.372*x7 + 1.1893141713454*x10)*x7 - 1.868*log(
1.86752460515164*x4 + 2.61699842799583*x7 + 1.868*x10)*x10 -
12.7287341082197*log(x2)*x2 - 45.8763409542885*log(x5)*x5 -
10.607456380675*log(x8)*x8 - 12.7287341082197*log(x3)*x3 -
45.8763409542885*log(x6)*x6 - 10.607456380675*log(x9)*x9 -
12.7287341082197*log(x4)*x4 - 45.8763409542885*log(x7)*x7 -
10.607456380675*log(x10)*x10) + objvar =E= 0;
e2.. x2 + x3 + x4 =E= 0.4;
e3.. x5 + x6 + x7 =E= 0.1;
e4.. x8 + x9 + x10 =E= 0.5;
* set non-default bounds
x2.lo = 1E-7; x2.up = 0.4;
x3.lo = 1E-7; x3.up = 0.4;
x4.lo = 1E-7; x4.up = 0.4;
x5.lo = 1E-7; x5.up = 0.1;
x6.lo = 1E-7; x6.up = 0.1;
x7.lo = 1E-7; x7.up = 0.1;
x8.lo = 1E-7; x8.up = 0.5;
x9.lo = 1E-7; x9.up = 0.5;
x10.lo = 1E-7; x10.up = 0.5;
* set non-default levels
x2.l = 0.0088;
x3.l = 0.33595;
x4.l = 0.05525;
x5.l = 0.00065;
x6.l = 0.00193;
x7.l = 0.09742;
x8.l = 0.30803;
x9.l = 0.147;
x10.l = 0.04497;
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