MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance prob06

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.17712434 p1 ( gdx sol ) (infeas: 4e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1.17712415 (ANTIGONE) 1.17712434 (BARON) 1.17712434 (COUENNE) 1.17712417 (GUROBI) 1.17712400 (LINDO) 1.17712434 (SCIP)
Referencesⓘ	Maranas, C D and Floudas, C A, Global Optimization in Generalized Geometric Programming, Computers and Chemical Engineering, 21:4, 1997, 351-369. 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ⓘ	QCP
#Variablesⓘ	2
#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ⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.2500e-02
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	0.2857
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

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


Variables  objvar,x2;

Equations  e1,e2;


e1.. 0.25*objvar - 0.0625*sqr(objvar) - 0.0625*sqr(x2) + 0.5*x2 =L= 1;

e2.. 0.0714285714285714*sqr(objvar) + 0.0714285714285714*sqr(x2) - 
     0.428571428571429*objvar - 0.428571428571429*x2 =L= -1;

* set non-default bounds
objvar.lo = 1; objvar.up = 5.5;
x2.lo = 1; x2.up = 5.5;

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;