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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e09

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
0.00000000 p1 ( gdx sol )
(infeas: 0)
-0.50000000 p2 ( gdx sol )
(infeas: 3e-10)
Other points (infeas > 1e-08)  
Dual Bounds
-0.50000000 (ANTIGONE)
-0.50000000 (BARON)
-0.50000000 (COUENNE)
-0.50000045 (GUROBI)
-0.50000000 (LINDO)
-0.50000001 (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.
Swaney, R E, Global solution of algebraic nonlinear programs, 1990. American Institute of Chemical Engineers, Annual Meeting, Chicago, IL.
Source BARON book instance misc/e09
Added to library 03 Sep 2002
Problem type QCQP
#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 1
#Linear Constraints 0
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 2
#Nonlinear Nonzeros in Jacobian 2
#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 2.0000e+00
Maximal coefficient 4.0000e+00
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        1        0        1        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
*          5        1        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x1,x2;

Equations  e1,e2;


e1.. 4*x1*x2 + 2*x1 + 2*x2 =L= 3;

e2.. 2*x1*x2 + objvar =E= 0;

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

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;


Last updated: 2022-08-11 Git hash: f176bd52
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