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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e19

Formats ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
11.00000000 p1 ( gdx sol )
(infeas: 0)
-86.42220510 p2 ( gdx sol )
(infeas: 0)
-118.70485980 p3 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-118.70486310 (ANTIGONE)
-118.70485990 (BARON)
-118.70486990 (COUENNE)
-118.70485980 (LINDO)
-118.70486090 (SCIP)
References Manousiouthakis, V and Sourlas, D, A Global Optimization Approach to Rationally Constrained Rational Programming, Chemical Engineering Communications, 115:1, 1992, 127-147.
Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Source BARON book instance misc/e19
Added to library 03 Sep 2002
Problem type NLP
#Variables 2
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type polynomial
Objective curvature nonconvex
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 2
#Linear Constraints 1
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature concave
#Nonzeros in Jacobian 4
#Nonlinear Nonzeros in Jacobian 1
#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 2.4000e+01
Infeasibility of initial point 2
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
*          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        4        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x2;

Equations  e1,e2,e3;


e1..  - x1 + x2 =L= 8;

e2.. (-sqr(x1)) - 2*x1 + x2 =L= -2;

e3.. -(POWER(x1,4) - 14*sqr(x1) + 24*x1 - sqr(x2)) + objvar =E= 0;

* set non-default bounds
x1.lo = -8; x1.up = 10;
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;


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