MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance mhw4d

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.02931083 p1 ( gdx sol ) (infeas: 9e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.02931083 (COUENNE) 0.02931083 (LINDO) 0.02930981 (SCIP)
Referencesⓘ	Wright, M H, Numerical Methods for Nonlinearly Constraint Optimization, PhD thesis, Stanford University, 1976.
Sourceⓘ	GAMS Model Library model mhw4d
Applicationⓘ	Test Problem
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	5
#Constraintsⓘ	3
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	5
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	15
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	5
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	4.0000e+00
Infeasibility of initial pointⓘ	2.243
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
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         14        4       10        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6;

Equations  e1,e2,e3,e4;


e1.. -(sqr((-1) + x2) + sqr(x2 - x3) + POWER(x3 - x4,3) + POWER(x4 - x5,4) + 
     POWER(x5 - x6,4)) + objvar =E= 0;

e2.. sqr(x3) + POWER(x4,3) + x2 =E= 6.24264068711929;

e3.. -sqr(x4) + x3 + x5 =E= 0.82842712474619;

e4.. x2*x6 =E= 2;

* set non-default levels
x2.l = -1;
x3.l = 2;
x4.l = 1;
x5.l = -2;
x6.l = -2;

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;