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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e37

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.97913912 p1 ( gdx sol )
(infeas: 0)
0.00104172 p2 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
0.00104167 (ANTIGONE)
0.00104172 (BARON)
0.00104172 (COUENNE)
0.00104171 (LINDO)
0.00104123 (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.
Beck, J V and Arnold, K J, Parameter Estimation in Engineering and Science, Wiley, New York, 1977.
Source BARON book instance misc/e37
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 nonlinear
Objective curvature nonconcave
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 1
#Linear Constraints 1
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions exp mul sqr
Constraints curvature linear
#Nonzeros in Jacobian 2
#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 1.2700e-02
Maximal coefficient 1.0000e+01
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
*          2        1        0        1        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      2
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        3        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar,x4,x5;

Positive Variables  x1,x2;

Equations  e1,e2;


e1..    x1 - x2 =L= 0;

e2.. -(sqr((-1.9837) + x4 + x5) + sqr((-0.8393) + exp(-x1)*x4 + exp(-x2)*x5) + 
     sqr((-0.4305) + exp(-2*x1)*x4 + exp(-2*x2)*x5) + sqr((-0.2441) + exp(-3*x1
     )*x4 + exp(-3*x2)*x5) + sqr((-0.1248) + exp(-4*x1)*x4 + exp(-4*x2)*x5) + 
     sqr((-0.0981) + exp(-5*x1)*x4 + exp(-5*x2)*x5) + sqr((-0.0549) + exp(-6*x1
     )*x4 + exp(-6*x2)*x5) + sqr((-0.0174) + exp(-7*x1)*x4 + exp(-7*x2)*x5) + 
     sqr((-0.0249) + exp(-8*x1)*x4 + exp(-8*x2)*x5) + sqr((-0.0154) + exp(-9*x1
     )*x4 + exp(-9*x2)*x5) + sqr((-0.0127) + exp(-10*x1)*x4 + exp(-10*x2)*x5))
      + objvar =E= 0;

* set non-default bounds
x1.up = 100;
x2.up = 100;
x4.fx = 1;
x5.fx = 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;


Last updated: 2022-04-26 Git hash: de668763
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