MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex5_2_4

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000000 p1 ( gdx sol ) (infeas: 0) -450.00000000 p2 ( gdx sol ) (infeas: 3e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-450.00000050 (ANTIGONE) -450.00000090 (BARON) -450.00026250 (COUENNE) -450.00000000 (GUROBI) -450.00000000 (LINDO) -450.00000080 (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. Ben-Tal, A, Eiger, G, and Gershovitz, V, Global Minimization by Reducing the Duality Gap, Mathematical Programming, 63:1, 1994, 193-212.
Sourceⓘ	Test Problem ex5.2.4 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	7
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	7
#Nonlinear Nonzeros in Objectiveⓘ	5
#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ⓘ	20
#Nonlinear Nonzeros in Jacobianⓘ	11
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	12
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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ⓘ	1.6000e+01
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        2        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          8        8        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         28       12       16        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2,x3,x4,x5,x6,x7;

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


e1.. -((9 - 6*x1 - 16*x2 - 15*x3)*x4 + (15 - 6*x1 - 16*x2 - 15*x3)*x5) + x6
      - 5*x7 - objvar =E= 0;

e2.. x3*x4 + x3*x5 =L= 50;

e3..    x4 + x6 =L= 100;

e4..    x5 + x7 =L= 200;

e5.. (-2.5 + 3*x1 + x2 + x3)*x4 - 0.5*x6 =L= 0;

e6.. (-1.5 + 3*x1 + x2 + x3)*x5 + 0.5*x7 =L= 0;

e7..    x1 + x2 + x3 =E= 1;

* set non-default bounds
x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 100;
x5.up = 200;
x6.up = 100;
x7.up = 200;

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;