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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e14

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
4.57958240 p1 ( gdx sol )
(infeas: 2e-16)
Other points (infeas > 1e-08)  
Dual Bounds
4.57958190 (ALPHAECP)
4.57958240 (ANTIGONE)
4.57958240 (BARON)
4.57958240 (BONMIN)
4.57958240 (COUENNE)
4.57958240 (LINDO)
4.57958240 (SCIP)
4.57958240 (SHOT)
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.
Yuan, X, Zhang, S, Pibouleau, L, and Domenech, S, Une méthode d'optimisation non linéaire en variables mixtes pour la conception de procédés, RAIRO - Operations Research, 22:4, 1988, 331-346.
Source BARON book instance e14
Added to library 01 Sep 2002
Problem type MBNLP
#Variables 11
#Binary Variables 4
#Integer Variables 0
#Nonlinear Variables 7
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature convex
#Nonzeros in Objective 7
#Nonlinear Nonzeros in Objective 7
#Constraints 13
#Linear Constraints 9
#Quadratic Constraints 4
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions log sqr
Constraints curvature convex
#Nonzeros in Jacobian 32
#Nonlinear Nonzeros in Jacobian 10
#Nonzeros in (Upper-Left) Hessian of Lagrangian 7
#Nonzeros in Diagonal of Hessian of Lagrangian 7
#Blocks in Hessian of Lagrangian 7
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 3.0000e+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
*         14        5        0        9        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12        8        4        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         40       23       17        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,b8,b9,b10,b11,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7;

Binary Variables  b8,b9,b10,b11;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14;


e1..    x1 + x2 + x3 + b8 + b9 + b10 =L= 5;

e2.. sqr(x6) + sqr(x1) + sqr(x2) + sqr(x3) =L= 5.5;

e3..    x1 + b8 =L= 1.2;

e4..    x2 + b9 =L= 1.8;

e5..    x3 + b10 =L= 2.5;

e6..    x1 + b11 =L= 1.2;

e7.. sqr(x5) + sqr(x2) =L= 1.64;

e8.. sqr(x6) + sqr(x3) =L= 4.25;

e9.. sqr(x5) + sqr(x3) =L= 4.64;

e10..    x4 - b8 =E= 0;

e11..    x5 - b9 =E= 0;

e12..    x6 - b10 =E= 0;

e13..    x7 - b11 =E= 0;

e14.. -(sqr((-1) + x4) + sqr((-2) + x5) + sqr((-1) + x6) - log(1 + x7) + sqr((-
      1) + x1) + sqr((-2) + x2) + sqr((-3) + x3)) + objvar =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.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 MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


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