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Instance prob06

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
1.17712434 p1 ( gdx sol )
(infeas: 4e-15)
Other points (infeas > 1e-08)  
Dual Bounds
1.17712415 (ANTIGONE)
1.17712434 (BARON)
1.17712434 (COUENNE)
1.17712417 (GUROBI)
1.17712400 (LINDO)
1.17712434 (SCIP)
References Maranas, C D and Floudas, C A, Global Optimization in Generalized Geometric Programming, Computers and Chemical Engineering, 21:4, 1997, 351-369.
Westerlund, Tapio and Lundqvist, Kurt, Alpha-ECP, Version 5.01 An Interactive MINLP-Solver Based on the Extended Cutting Plane Method, Tech. Rep. 01-178-A, Process Design Laboratory at Abo University, 2001.
Source Example models from AlphaECP
Added to library 31 Jul 2001
Problem type QCP
#Variables 2
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 2
#Linear Constraints 0
#Quadratic Constraints 2
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 4
#Nonlinear Nonzeros in Jacobian 4
#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 6.2500e-02
Maximal coefficient 1.0000e+00
Infeasibility of initial point 0.2857
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
*          2        0        0        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          2        2        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          4        0        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2;

Equations  e1,e2;


e1.. 0.25*objvar - 0.0625*sqr(objvar) - 0.0625*sqr(x2) + 0.5*x2 =L= 1;

e2.. 0.0714285714285714*sqr(objvar) + 0.0714285714285714*sqr(x2) - 
     0.428571428571429*objvar - 0.428571428571429*x2 =L= -1;

* set non-default bounds
objvar.lo = 1; objvar.up = 5.5;
x2.lo = 1; x2.up = 5.5;

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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