MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex1226

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-17. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-17. (ANTIGONE) -17. (BARON) -17. (COUENNE) -17. (LINDO) -17. (SCIP) -21. (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. Pörn, Ray, Harjunkoski, Iiro, and Westerlund, Tapio, Convexification of Different Classes of Non-Convex MINLP Problems, Computers and Chemical Engineering, 23:3, 1999, 439-448.
Sourceⓘ	Test Problem ex12.2.6 of Chapter 12 of Floudas e.a. handbook
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	5
#Binary Variablesⓘ	3
#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ⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	5
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	1
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	12
#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ⓘ	5.0000e-01
Maximal coefficientⓘ	1.1000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        2        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        3        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         15       13        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,b3,b4,b5,objvar;

Binary Variables  b3,b4,b5;

Equations  e1,e2,e3,e4,e5,e6;


e1.. 8*x1 - 2*x1**0.5*sqr(x2) + 11*x2 + 2*sqr(x2) - 2*x2**0.5 =L= 39;

e2..    x1 - x2 =L= 3;

e3..    3*x1 + 2*x2 =L= 24;

e4..    x2 - b3 - 2*b4 - 4*b5 =E= 1;

e5..    b4 + b5 =L= 1;

e6..    5*x1 - 3*x2 + objvar =E= 0;

* set non-default bounds
x1.lo = 1; x1.up = 10;
x2.lo = 1; x2.up = 6;

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;