MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_glmp_fp2

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7.62750000 p1 ( gdx sol ) (infeas: 0) 7.34454542 p2 ( gdx sol ) (infeas: 6e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	7.34454541 (ANTIGONE) 7.34454541 (BARON) 7.34454542 (COUENNE) 7.34454542 (CPLEX) 7.34454540 (GUROBI) 7.34454542 (LINDO) 7.34454542 (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. Falk, J E and Polocsay, S W, Image space analysis of generalized fractional programs, Journal of Global Optimization, 4:1, 1994, 63-88.
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ⓘ	9
#Linear Constraintsⓘ	9
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	20
#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ⓘ	2.0000e+00
Infeasibility of initial pointⓘ	7
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        3        2        5        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
*         23       21        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1..    2*x1 + x2 =L= 14;

e2..    x1 + x2 =L= 10;

e3..    1.44*x1 + x2 =G= 4.89;

e4..  - 1.58*x1 + x2 =L= 5.65;

e5..  - 1.03*x1 + x2 =L= 5.93;

e6..    x1 + 2*x2 =G= 6;

e7..    x1 - x2 =L= 3;

e8.. -x3*x4 + objvar =E= 0;

e9..    x1 + x2 - x3 =E= 0;

e10..    x1 - x2 - x4 =E= -7;

* set non-default bounds
x1.up = 5;
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;