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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e25

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
0.89019359 p1 ( gdx sol )
(infeas: 4e-16)
Other points (infeas > 1e-08)  
Dual Bounds
0.89019359 (ANTIGONE)
0.89019359 (BARON)
0.89019359 (COUENNE)
0.89019359 (CPLEX)
0.89019359 (GUROBI)
0.89019359 (LINDO)
0.89019352 (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.
Thoai, N V, A global optimization approach for solving convex multiplicative programming problems, Journal of Global Optimization, 1:4, 1991, 341-357.
Source BARON book instance misc/e25
Added to library 03 Sep 2002
Problem type QP
#Variables 4
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 8
#Linear Constraints 8
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 32
#Nonlinear Nonzeros in Jacobian 0
#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 6.0581e-02
Maximal coefficient 9.8309e-01
Infeasibility of initial point 1.354
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
*          9        1        0        8        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
*         37       33        4        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,e9;


e1..    0.488509*x1 + 0.063565*x2 + 0.945686*x3 + 0.210704*x4 =L= 3.562809;

e2..  - 0.324014*x1 - 0.501754*x2 - 0.719204*x3 + 0.099562*x4 =L= -0.052215;

e3..    0.445225*x1 - 0.346896*x2 + 0.637939*x3 - 0.257623*x4 =L= 0.42792;

e4..  - 0.202821*x1 + 0.647361*x2 + 0.920135*x3 + 0.983091*x4 =L= 0.84095;

e5..  - 0.88642*x1 - 0.802444*x2 - 0.305441*x3 - 0.180123*x4 =L= -1.353686;

e6..  - 0.515399*x1 - 0.42482*x2 + 0.897498*x3 + 0.187268*x4 =L= 2.137251;

e7..  - 0.591515*x1 + 0.060581*x2 - 0.427365*x3 + 0.579388*x4 =L= -0.290987;

e8..    0.423524*x1 + 0.940496*x2 - 0.437944*x3 - 0.742941*x4 =L= 0.37362;

e9.. -(0.217796 + 0.813396*x1 + 0.67444*x2 + 0.305038*x3 + 0.129742*x4)*(
     0.091947 + 0.224508*x1 + 0.063458*x2 + 0.93223*x3 + 0.528736*x4) + objvar
      =E= 0;

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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