MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance prob09

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000000 p1 ( gdx sol ) (infeas: 1e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) -0.00000000 (BARON) -0.00000000 (COUENNE) -0.00000000 (LINDO) -0.00000000 (SCIP)
Referencesⓘ	Westerlund, Tapio and Lundqvist, Kurt, Alpha-ECP, Version 5.01 An Interactive MINLP-Solver Based on the Extended Cutting Plane Method, Tech. Rep. 01-178-A, Process Design Laboratory at Abo University, 2001.
Sourceⓘ	Example models from AlphaECP
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#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ⓘ	1
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	3
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+02
Infeasibility of initial pointⓘ	7.996e-19
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          3        1        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3;

Equations  e1;


e1.. 100*sqr(x3 - sqr(x2)) + sqr(1 - x2) - objvar =E= 0;

* set non-default bounds
objvar.lo = -100; objvar.up = 100;
x2.lo = -2; x2.up = 2;
x3.lo = -2; x3.up = 2;

* set non-default levels
objvar.l = 2.28067255148468E-6;
x2.l = 0.999139149741104;
x3.l = 0.998154959548312;

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;