MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance st_e18

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-2.82842713 p1 ( gdx sol )
(infeas: 4e-10)
Other points (infeas > 1e-08)  
Dual Bounds
-2.82842713 (ANTIGONE)
-2.82842723 (BARON)
-2.82842713 (COUENNE)
-2.82842713 (GUROBI)
-2.82842713 (LINDO)
-2.82842713 (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.
Visweswaran, V and Floudas, C A, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs -- II. Applications of theory and test problems, Computers and Chemical Engineering, 14:12, 1990, 1419-1434.
Source BARON book instance misc/e18
Added to library 03 Sep 2002
Problem type QCP
#Variables 2
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 0
#Constraints 4
#Linear Constraints 2
#Quadratic Constraints 2
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 8
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 1.0000e+00
Infeasibility of initial point 1
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
*          5        1        0        4        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
*         11        7        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Equations  e1,e2,e3,e4,e5;


e1.. -(sqr(x1) + sqr(x2)) =L= -1;

e2.. sqr(x1) + sqr(x2) =L= 4;

e3..  - x1 + x2 =L= 1;

e4..    x1 - x2 =L= 1;

e5..  - x1 - x2 + objvar =E= 0;

* set non-default bounds
x1.lo = -2; x1.up = 2;
x2.lo = -2; x2.up = 2;

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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0