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Instance st_e41

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
641.82356230 p1 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
641.82356170 (ANTIGONE)
641.82356100 (BARON)
641.82315590 (COUENNE)
641.82345950 (LINDO)
641.82355980 (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.
Kim, Y S, Problems in reliability, 1998. Personal Communication.
Source BARON book instance misc/e41
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 signomial
Objective curvature concave
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 2
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 2
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 8
#Nonlinear Nonzeros in Jacobian 8
#Nonzeros in (Upper-Left) Hessian of Lagrangian 16
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.0000e-01
Maximal coefficient 3.0000e+02
Infeasibility of initial point 0.1266
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
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         13        1       12        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Equations  e1,e2,e3;


e1.. -(-sqr(1 - x1)*x3*sqr(1 - x4) - sqr(1 - (1 - (1 - x1)*(1 - x4))*x2)*(1 - 
     x3)) =L= 0.1;

e2.. (-sqr(1 - x1)*x3*sqr(1 - x4)) - sqr(1 - (1 - (1 - x1)*(1 - x4))*x2)*(1 - 
     x3) =L= 0;

e3.. -(200*x1**0.6 + 200*x2**0.6 + 200*x3**0.6 + 300*x4**0.6) + objvar =E= 0;

* set non-default bounds
x1.lo = 0.5; x1.up = 1;
x2.lo = 0.5; x2.up = 1;
x3.lo = 0.5; x3.up = 1;
x4.lo = 0.5; x4.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 NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


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