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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e04

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
5194.86624400 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
5194.86623900 (ANTIGONE)
5194.86623900 (BARON)
5194.86624400 (COUENNE)
5194.86624400 (LINDO)
5194.86624400 (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.
Stoecker, W F, Design of Thermal Systems, McGraw Hill Book Co., New York, 1971.
Source BARON book instance misc/e04
Added to library 03 Sep 2002
Problem type NLP
#Variables 4
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 2
#Constraints 2
#Linear Constraints 0
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 1
Operands in Gen. Nonlin. Functions div exp vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 5
#Nonlinear Nonzeros in Jacobian 3
#Nonzeros in (Upper-Left) Hessian of Lagrangian 5
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 1.333333
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 9.0000e-01
Maximal coefficient 3.9500e+03
Infeasibility of initial point 1.152e+04
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        2        1        0        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
*          9        4        5        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x3;

Equations  e1,e2,e3;


e1.. x3*x1 + 144*x4 =G= 11520;

e2.. -exp(11.86 - 3950/(460 + x4)) + x2 =E= 0;

e3.. -(400*x1**0.9 + 22*(-14.7 + x2)**1.2) - x3 + objvar =E= 1000;

* set non-default bounds
x1.up = 15.1;
x2.lo = 14.7; x2.up = 94.2;
x3.up = 5371;
x4.lo = -459.67; x4.up = 80;

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;


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