MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_glmp_kky

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.50000000 p1 ( gdx sol ) (infeas: 0) -2.50000000 p2 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-2.50000000 (ANTIGONE) -2.50000000 (BARON) -2.50000000 (COUENNE) -2.50000000 (CPLEX) -2.50000005 (GUROBI) -2.50000000 (LINDO) -2.50000000 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Konno, H, Kuno, T, and Yajima, Y, Global optimization of a generalized convex multiplicative function, Journal of Global Optimization, 4:1, 1994, 47-62.
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QP
#Variablesⓘ	7
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	13
#Linear Constraintsⓘ	13
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	31
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	8.0000e+00
Infeasibility of initial pointⓘ	10
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         14        6        0        8        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
*         37       33        4        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14;


e1..  - 5*x1 + 8*x2 =L= 24;

e2..  - 5*x1 - 8*x2 =L= 100;

e3..  - 6*x1 + 3*x2 =L= 100;

e4..  - 4*x1 - 5*x2 =L= -10;

e5..    5*x1 - 8*x2 =L= 100;

e6..    5*x1 + 8*x2 =L= 44;

e7..    6*x1 - 3*x2 =L= 15;

e8..    4*x1 + 5*x2 =L= 100;

e9.. -(x4*x5 + x6*x7) - x3 + objvar =E= 0;

e10..    3*x1 - 4*x2 - x3 =E= 0;

e11..    x1 + 2*x2 - x4 =E= 1.5;

e12..    2*x1 - x2 - x5 =E= -4;

e13..    x1 - 2*x2 - x6 =E= -8.5;

e14..    2*x1 + x2 - x7 =E= 1;

* set non-default bounds
x1.up = 10;
x2.up = 10;

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;