MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex7_3_1

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.34173955 p1 ( gdx sol ) (infeas: 1e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.34173955 (ANTIGONE) 0.34173955 (BARON) 0.34173955 (COUENNE) 0.34173955 (LINDO) 0.34173955 (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. de Gaston, R R E and Safonov, M G, Exact Calculation of the Multi-Loop Stability Margin, IEEE Transactions on Automatic Control, 33:2, 1988, 156-171.
Sourceⓘ	Test Problem ex7.3.1 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	4
#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ⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	7
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	15
#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ⓘ	1.0000e+03
Infeasibility of initial pointⓘ	800
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        1        0        7        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17       14        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2,x3,x4;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1..  - x4 + objvar =E= 0;

e2.. 10*sqr(x2)*POWER(x3,3) + 10*POWER(x2,3)*sqr(x3) + 200*sqr(x2)*sqr(x3) + 
     100*POWER(x2,3)*x3 + 100*POWER(x3,3)*x2 + x1*x2*sqr(x3) + sqr(x2)*x1*x3 + 
     1000*sqr(x3)*x2 + 8*sqr(x3)*x1 + 1000*sqr(x2)*x3 + 8*sqr(x2)*x1 + 6*x1*x2*
     x3 - sqr(x1) + 60*x1*x3 + 60*x1*x2 - 200*x1 =L= 0;

e3..  - x1 - 800*x4 =L= -800;

e4..    x1 - 800*x4 =L= 800;

e5..  - x2 - 2*x4 =L= -4;

e6..    x2 - 2*x4 =L= 4;

e7..  - x3 - 3*x4 =L= -6;

e8..    x3 - 3*x4 =L= 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;