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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex7_3_1

Formats ams gms mod nl osil pip
Primal Bounds
0.34173955 p1 ( gdx sol )
(infeas: 1e-13)
Dual Bounds
0.34173955 (ANTIGONE)
0.34173955 (BARON)
0.34173955 (COUENNE)
0.34173955 (LINDO)
0.34173947 (SCIP)
References Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999.
de Gaston, R R E and Safonov, M G, Exact Calculation of the Multi-Loop Stability Margin, IEEE Transactions on Automatic Control, 33:2, 1988, 156-171.
Source Test Problem ex7.3.1 of Chapter 7 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 4
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 3
#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 7
#Linear Constraints 6
#Quadratic Constraints 0
#Polynomial Constraints 1
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 15
#Nonlinear Nonzeros in Jacobian 3
#Nonzeros in (Upper-Left) Hessian of Lagrangian 9
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 800
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
*          8        1        0        7        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
*         17       14        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2,x3,x4;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1..  - x4 + objvar =E= 0;

e2.. 10*sqr(x2)*POWER(x3,3) + 10*POWER(x2,3)*sqr(x3) + 200*sqr(x2)*sqr(x3) + 
     100*POWER(x2,3)*x3 + 100*POWER(x3,3)*x2 + x1*x2*sqr(x3) + sqr(x2)*x1*x3 + 
     1000*sqr(x3)*x2 + 8*sqr(x3)*x1 + 1000*sqr(x2)*x3 + 8*sqr(x2)*x1 + 6*x1*x2*
     x3 - sqr(x1) + 60*x1*x3 + 60*x1*x2 - 200*x1 =L= 0;

e3..  - x1 - 800*x4 =L= -800;

e4..    x1 - 800*x4 =L= 800;

e5..  - x2 - 2*x4 =L= -4;

e6..    x2 - 2*x4 =L= 4;

e7..  - x3 - 3*x4 =L= -6;

e8..    x3 - 3*x4 =L= 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: 2018-09-14 Git hash: ac5a5314
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