MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex1223a

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	4.57958240 p1 ( gdx sol ) (infeas: 2e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	4.57958240 (ALPHAECP) 4.57958240 (ANTIGONE) 4.57958240 (BARON) 4.57958240 (BONMIN) 4.57958240 (COUENNE) 4.57958239 (CPLEX) 4.57958240 (GUROBI) 4.57958240 (LINDO) 4.57958240 (SCIP) 4.57958240 (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. Yuan, X, Zhang, S, Pibouleau, L, and Domenech, S, Une méthode d'optimisation non linéaire en variables mixtes pour la conception de procédés, RAIRO - Operations Research, 22:4, 1988, 331-346.
Sourceⓘ	modified Test Problem ex12.2.3 of Chapter 12 of Floudas e.a. handbook
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBQCQP
#Variablesⓘ	7
#Binary Variablesⓘ	4
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	7
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	9
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	24
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	3
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	3
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ⓘ	6.9315e-01
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        1        0        9        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          8        4        4        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         32       23        9        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,b4,b5,b6,b7,objvar;

Positive Variables  x1,x2,x3;

Binary Variables  b4,b5,b6,b7;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1..    x1 + x2 + x3 + b4 + b5 + b6 =L= 5;

e2.. sqr(x1) + sqr(x2) + sqr(x3) + b6 =L= 5.5;

e3..    x1 + b4 =L= 1.2;

e4..    x2 + b5 =L= 1.8;

e5..    x3 + b6 =L= 2.5;

e6..    x1 + b7 =L= 1.2;

e7.. sqr(x2) + b5 =L= 1.64;

e8.. sqr(x3) + b6 =L= 4.25;

e9.. sqr(x3) + b5 =L= 4.64;

e10.. -(sqr((-1) + x1) + sqr((-2) + x2) + sqr((-3) + x3)) + b4 + 3*b5 + b6
       + 0.693147180559945*b7 + objvar =E= 6;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;

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;