MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex1222

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.07654308 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1.07654308 (ANTIGONE) 1.07654308 (BARON) 1.07654308 (COUENNE) 1.07654308 (LINDO) 1.07654308 (SCIP) 0.10000000 (SHOT)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Floudas, C A, Nonlinear and Mixed Integer Optimization: Fundamentals and Applications, Oxford University Press, 1995.
Sourceⓘ	Test Problem ex12.2.2 of Chapter 12 of Floudas e.a. handbook
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	3
#Binary Variablesⓘ	1
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	1
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	1
#Constraintsⓘ	3
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	1
Operands in Gen. Nonlin. Functionsⓘ	exp
Constraints curvatureⓘ	concave
#Nonzeros in Jacobianⓘ	6
#Nonlinear Nonzeros in Jacobianⓘ	1
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	1
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	2.0000e-01
Maximal coefficientⓘ	5.0000e+00
Infeasibility of initial pointⓘ	0.2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        1        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        3        1        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          9        7        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,b3,objvar;

Binary Variables  b3;

Equations  e1,e2,e3,e4;


e1.. -exp((-0.2) + x1) - x2 =L= 0;

e2..    x2 + 1.1*b3 =L= -1;

e3..    x1 - 1.2*b3 =L= 0;

e4.. -5*sqr((-0.5) + x1) + 0.7*b3 + objvar =E= 0.8;

* set non-default bounds
x1.lo = 0.2; x1.up = 1;
x2.lo = -2.22554; x2.up = -1;

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;