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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e21

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.00000000 p1 ( gdx sol )
(infeas: 0)
-13.40190356 p2 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-13.40190357 (ANTIGONE)
-13.40190358 (BARON)
-13.40190356 (COUENNE)
-13.40190356 (LINDO)
-13.40190356 (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.
Stephanopoulos, G and Westerberg, A W, The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization, Journal of Optimization Theory and Applications, 15:3, 1975, 285-309.
Source BARON book instance misc/e21
Added to library 03 Sep 2002
Problem type NLP
#Variables 6
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature concave
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 3
#Constraints 6
#Linear Constraints 6
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 14
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 3
#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 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 4.0000e-01
Maximal coefficient 5.0000e+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
*          7        4        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21       18        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,objvar;

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

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - 3*x1 + x2 - 3*x4 =E= 0;

e2..  - 2*x2 + x3 - 2*x5 =E= 0;

e3..    4*x4 - x6 =E= 0;

e4..    x1 + 2*x4 =L= 4;

e5..    x2 + x5 =L= 4;

e6..    x3 + x6 =L= 6;

e7.. -(x1**0.6 + x2**0.6 + x3**0.4 - 4*x3) - 2*x4 - 5*x5 + x6 + objvar =E= 0;

* set non-default bounds
x1.up = 3;
x2.up = 4;
x3.up = 4;
x4.up = 2;
x5.up = 2;
x6.up = 6;

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: 2022-04-26 Git hash: de668763
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