MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance prob03

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	10.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	10.00000000 (ANTIGONE) 10.00000000 (BARON) 10.00000000 (COUENNE) 10.00000000 (CPLEX) 10.00000000 (GUROBI) 10.00000000 (LINDO) 10.00000000 (SCIP) 10.00000000 (SHOT)
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. Still, Claus and Westerlund, Tapio, Extended Cutting Plane Algorithm. In Floudas, C A and Paradalos, Panos M, Encyclopedia of Optimization, Kluwer Academic Press, 2001, 593-601.
Sourceⓘ	Example models from AlphaECP
Added to libraryⓘ	02 Jul 2003
Problem typeⓘ	IQCP
#Variablesⓘ	2
#Binary Variablesⓘ	0
#Integer Variablesⓘ	2
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	2
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	1
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	2
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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ⓘ	2.0000e+00
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	2.5
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        1        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        1        0        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          5        3        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,objvar;

Integer Variables  i1,i2;

Equations  e1,e2;


e1..  - 3*i1 - 2*i2 + objvar =E= 0;

e2.. -i1*i2 =L= -3.5;

* set non-default bounds
i1.lo = 1; i1.up = 5;
i2.lo = 1; i2.up = 5;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;