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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex3_1_4

Formats ams gms lp mod nl osil pip
Primal Bounds
-4.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-4.00000000 (ANTIGONE)
-4.00000003 (BARON)
-4.00000000 (COUENNE)
-4.00000000 (LINDO)
-4.00000000 (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.
Ben-Sadd, S, An Algorithm for a Class of Nonlinear Nonconvex Optimization Problems, PhD thesis, University of California, Los Angeles, 1989.
Source Test Problem ex3.1.4 of Chapter 3 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type QCP
#Variables 3
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 0
#Constraints 3
#Linear Constraints 2
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature concave
#Nonzeros in Jacobian 8
#Nonlinear Nonzeros in Jacobian 3
#Nonzeros in (Upper-Left) Hessian of Lagrangian 9
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0
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        1        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         12        9        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,objvar;

Positive Variables  x1,x2,x3;

Equations  e1,e2,e3,e4;


e1..    2*x1 - x2 + x3 + objvar =E= 0;

e2.. x1*(4*x1 - 2*x2 + 2*x3) + x2*(2*x2 - 2*x1 - x3) + x3*(2*x1 - x2 + 2*x3) - 
     20*x1 + 9*x2 - 13*x3 =G= -24;

e3..    x1 + x2 + x3 =L= 4;

e4..    3*x2 + x3 =L= 6;

* set non-default bounds
x1.up = 2;
x3.up = 3;

* set non-default levels
x1.l = 0.5;
x3.l = 3;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


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