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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex7_2_2

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.37461370 p1 ( gdx sol ) (infeas: 8e-16) -0.38881143 p2 ( gdx sol ) (infeas: 3e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.38881162 (ANTIGONE) -0.38881181 (BARON) -0.38881143 (COUENNE) -0.38881145 (LINDO) -0.38881203 (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. Ryoo, H S and Sahinidis, N V, Global Optimization of Nonconvex NLPs and MINLPs with Applications in Process Design, Computers and Chemical Engineering, 19:5, 1995, 551-566. Manousiouthakis, V and Sourlas, D, A Global Optimization Approach to Rationally Constrained Rational Programming, Chemical Engineering Communications, 115:1, 1992, 127-147. Maranas, C D and Floudas, C A, Global Optimization in Generalized Geometric Programming, Computers and Chemical Engineering, 21:4, 1997, 351-369.
Sourceⓘ	Test Problem ex7.2.2 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	6
#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ⓘ	5
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	1
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	15
#Nonlinear Nonzeros in Jacobianⓘ	10
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
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ⓘ	3.5272e-02
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        5        0        1        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
*         17        7       10        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2,x3,x4;

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


e1..    x4 + objvar =E= 0;

e2.. 0.09755988*x1*x5 + x1 =E= 1;

e3.. 0.0965842812*x2*x6 + x2 - x1 =E= 0;

e4.. 0.0391908*x3*x5 + x3 + x1 =E= 1;

e5.. 0.03527172*x4*x6 + x4 - x1 + x2 - x3 =E= 0;

e6.. x5**0.5 + x6**0.5 =L= 4;

* set non-default bounds
x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.lo = 1E-5; x5.up = 16;
x6.lo = 1E-5; x6.up = 16;

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;