MINLPLib

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 py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-4.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-4.00000000 (ANTIGONE) -4.00000002 (BARON) -4.00000000 (COUENNE) -4.00000006 (GUROBI) -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
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	2.0000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity 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;