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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex1222

Formats ams gms mod nl osil
Primal Bounds
1.07654308 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
1.07654308 (ANTIGONE)
1.07654308 (BARON)
1.07654308 (COUENNE)
1.07654308 (LINDO)
1.07654100 (SCIP)
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
Infeasibility of initial point 0.2
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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;


Last updated: 2018-09-14 Git hash: ac5a5314
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