MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_glmp_kk92

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 0) -9.00000000 p2 ( gdx sol ) (infeas: 3e-10) -12.00000000 p3 ( gdx sol ) (infeas: 6e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-12.00000001 (ANTIGONE) -12.00000001 (BARON) -12.00000000 (COUENNE) -12.00000000 (CPLEX) -12.00000000 (GUROBI) -12.00000000 (LINDO) -12.00000000 (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 and Kuno, T, Linear multiplicative programming, Mathematical Programming, 56:1, 1992, 51-64.
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	8
#Linear Constraintsⓘ	8
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	18
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	4.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          9        3        0        6        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
*         21       19        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar,x4,x5;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9;


e1..  - 4*x1 + x2 =L= 12;

e2..  - 4*x1 - 2*x2 =L= 12;

e3..    x1 - 2*x2 =L= 6;

e4..    x1 - x2 =L= 3;

e5..    x1 + x2 =L= 2;

e6..    2*x1 + x2 =L= 2;

e7.. -x4*x5 + objvar =E= 0;

e8..    x1 + x2 - x4 =E= 0;

e9..    x1 - x2 - x5 =E= 0;

* set non-default bounds
x1.lo = -3; x1.up = 1;
x2.lo = -3; x2.up = 4;

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;