MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance hs62

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-26272.54101000 p1 ( gdx sol ) (infeas: 3e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-26278.31113000 (ANTIGONE) -26272.58268000 (BARON) -26277.81464000 (COUENNE) -26272.70072000 (LINDO) -26273.91314000 (SCIP)
Referencesⓘ	Hock, W and Schittkowski, K, Test Examples for Nonlinear Programming Codes, Springer Verlag, 1981.
Sourceⓘ	GAMS Model Library model hs62
Applicationⓘ	Test Problem
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	1
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div log
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	3
#Nonlinear Nonzeros in Jacobianⓘ	3
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	3.0000e-02
Maximal coefficientⓘ	2.9000e+02
Infeasibility of initial pointⓘ	20
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        2        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        1        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4;

Positive Variables  x2,x3,x4;

Equations  e1,e2;


e1.. 32.174*(255*log((0.03 + x2 + x3 + x4)/(0.03 + 0.09*x2 + x3 + x4)) + 280*
     log((0.03 + x3 + x4)/(0.03 + 0.07*x3 + x4)) + 290*log((0.03 + x4)/(0.03 + 
     0.13*x4))) + objvar =E= 0;

e2.. 20*sqr((-1) + x2 + x3 + x4) =E= 0;

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;