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Instance ex8_1_7

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.02931083 p1 ( gdx sol ) (infeas: 6e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.02931060 (ANTIGONE) 0.02931083 (BARON) 0.02931083 (COUENNE) 0.02931083 (LINDO) 0.02931011 (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. Adjiman, C S, Dallwig, S, Floudas, C A, and Neumaier, A, A Global Optimization Method, alpha-BB, For General Twice-Differentiable NLPs - I. Theoretical Advances, Computers and Chemical Engineering, 22:9, 1998, 1137-1158. Murtagh, B A and Saunders, M A, MINOS 5.4 User's Guide, Tech. Rep., Systems Optimization Laboratory, Department of Operations Research, 1993.
Sourceⓘ	Test Problem ex8.1.7 of Chapter 8 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	5
#Constraintsⓘ	5
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	2
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	14
#Nonlinear Nonzeros in Jacobianⓘ	8
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	15
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	5
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	4.0000e+00
Infeasibility of initial pointⓘ	6.243
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        2        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         20        7       13        0
*
*  Solve m using NLP minimizing objvar;


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

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


e1.. sqr(x2) + POWER(x3,3) + x1 =L= 6.24264068711929;

e2.. (-POWER(x3,3)) - sqr(x2) - x1 =L= -6.24264068711929;

e3.. -sqr(x3) + x2 + x4 =L= 0.82842712474619;

e4.. sqr(x3) - x2 - x4 =L= -0.82842712474619;

e5.. 0.5*x1*x5 + 0.5*x1*x5 =E= 2;

e6.. -(sqr((-1) + x1) + sqr(x1 - x2) + POWER(x2 - x3,3) + POWER(x3 - x4,4) + 
     POWER(x4 - x5,4)) + objvar =E= 0;

* set non-default bounds
x1.lo = -5; x1.up = 5;
x2.lo = -5; x2.up = 5;
x3.lo = -5; x3.up = 5;
x4.lo = -5; x4.up = 5;
x5.lo = -5; x5.up = 5;

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;