MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex1221

Formats ams gms mod nl osil
Primal Bounds
7.66718007 p1 ( gdx sol )
(infeas: 2e-16)
Dual Bounds
7.66718007 (ANTIGONE)
7.66718007 (BARON)
7.66718007 (COUENNE)
7.66718007 (LINDO)
7.66718007 (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.
Kocis, Gary R and Grossmann, I E, Global Optimization of Nonconvex MINLP Problems in Process Synthesis, Industrial and Engineering Chemistry Research, 27:8, 1988, 1407-1421.
Source Test Problem ex12.2.1 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 5
#Nonlinear Nonzeros in Objective 0
#Constraints 5
#Linear Constraints 3
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 1
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 11
#Nonlinear Nonzeros in Jacobian 2
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 2
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 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
*          6        3        0        3        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
*         17       15        2        0
*
*  Solve m using MINLP minimizing objvar;


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

Positive Variables  x1,x2;

Binary Variables  b3,b4,b5;

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


e1..  - 2*x1 - 3*x2 - 1.5*b3 - 2*b4 + 0.5*b5 + objvar =E= 0;

e2.. sqr(x1) + b3 =E= 1.25;

e3.. x2**1.5 + 1.5*b4 =E= 3;

e4..    x1 + b3 =L= 1.6;

e5..    1.333*x2 + b4 =L= 3;

e6..  - b3 - b4 + b5 =L= 0;

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

* set non-default levels
x1.l = 1;
x2.l = 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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