MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex3_1_1

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7049.24802100 p1 ( gdx sol ) (infeas: 3e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	7049.24798000 (ANTIGONE) 7049.24801300 (BARON) 7049.24801800 (COUENNE) 7049.24796900 (GUROBI) 7049.24802000 (LINDO) 7049.24802100 (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. Hock, W and Schittkowski, K, Test Examples for Nonlinear Programming Codes, Springer Verlag, 1981.
Sourceⓘ	Test Problem ex3.1.1 of Chapter 3 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	8
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	8
#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ⓘ	6
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	17
#Nonlinear Nonzeros in Jacobianⓘ	8
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	2.666667
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.5000e-03
Maximal coefficientⓘ	2.5000e+03
Infeasibility of initial pointⓘ	8
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        1        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        9        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21       13        8        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7;


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

e2..    0.0025*x4 + 0.0025*x6 =L= 1;

e3..  - 0.0025*x4 + 0.0025*x5 + 0.0025*x7 =L= 1;

e4..  - 0.01*x5 + 0.01*x8 =L= 1;

e5.. 100*x1 - x1*x6 + 833.33252*x4 =L= 83333.333;

e6.. x2*x4 - x2*x7 - 1250*x4 + 1250*x5 =L= 0;

e7.. x3*x5 - x3*x8 - 2500*x5 =L= -1250000;

* set non-default bounds
x1.lo = 100; x1.up = 10000;
x2.lo = 1000; x2.up = 10000;
x3.lo = 1000; x3.up = 10000;
x4.lo = 10; x4.up = 1000;
x5.lo = 10; x5.up = 1000;
x6.lo = 10; x6.up = 1000;
x7.lo = 10; x7.up = 1000;
x8.lo = 10; x8.up = 1000;

* set non-default levels
x1.l = 579.19;
x2.l = 1360.13;
x3.l = 5109.92;
x4.l = 182.01;
x5.l = 295.6;
x6.l = 217.99;
x7.l = 286.4;
x8.l = 395.6;

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;