MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_4

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-11.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-11.00000001 (ANTIGONE) -11.00000001 (BARON) -11.00000000 (COUENNE) -11.00000000 (CPLEX) -11.00000000 (GUROBI) -11.00000000 (LINDO) -11.00000000 (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.
Sourceⓘ	Test Problem ex2.1.4 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	1
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	1
#Constraintsⓘ	5
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	30
#Nonlinear Nonzeros in Jacobianⓘ	0
#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
Minimal coefficientⓘ	1.0000e-01
Maximal coefficientⓘ	8.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        1        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         37       36        1        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6;

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


e1.. -(6.5*x1 - 0.5*x1*x1) + x2 + 2*x3 + 3*x4 + 2*x5 + x6 + objvar =E= 0;

e2..    x1 + 2*x2 + 8*x3 + x4 + 3*x5 + 5*x6 =L= 16;

e3..  - 8*x1 - 4*x2 - 2*x3 + 2*x4 + 4*x5 - x6 =L= -1;

e4..    2*x1 + 0.5*x2 + 0.2*x3 - 3*x4 - x5 - 4*x6 =L= 24;

e5..    0.2*x1 + 2*x2 + 0.1*x3 - 4*x4 + 2*x5 + 2*x6 =L= 12;

e6..  - 0.1*x1 - 0.5*x2 + 2*x3 + 5*x4 - 5*x5 + 3*x6 =L= 3;

* set non-default bounds
x1.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 2;

* set non-default levels
x2.l = 6;
x4.l = 1;
x5.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 NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;