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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e23

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1.00000000 p1 ( gdx sol ) (infeas: 0) -1.08333333 p2 ( gdx sol ) (infeas: 2e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.08333333 (ANTIGONE) -1.08333333 (BARON) -1.08333333 (COUENNE) -1.08333333 (CPLEX) -1.08333381 (GUROBI) -1.08333333 (LINDO) -1.08333338 (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. Al-Khayyal, F A and Falk, J E, Jointly Constrained Biconvex Programming, Mathematics of Operations Research, 8:2, 1983, 273-286.
Sourceⓘ	BARON book instance misc/e23
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QP
#Variablesⓘ	2
#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ⓘ	2
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	4
#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ⓘ	8.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        1        0        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        5        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x1,x2;

Equations  e1,e2,e3;


e1..  - 6*x1 + 8*x2 =L= 3;

e2..    3*x1 - x2 =L= 3;

e3.. -(x1*x2 - x1 - x2) + objvar =E= 0;

* set non-default bounds
x1.up = 5;
x2.up = 5;

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;