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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e38

Formats ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
7197.72714900 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
7197.72714900 (ANTIGONE)
7197.72714900 (BARON)
7197.72714900 (COUENNE)
7197.72714900 (LINDO)
7197.72714900 (SCIP)
3422.67454400 (SHOT)
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.
Sandgren, E, Nonlinear Integer and Discrete Programming in Mechanical Design Optimization, Journal of Mechanical Design, 112:2, 1990, 223-229.
Source BARON book instance misc/e38
Added to library 01 Sep 2002
Problem type MINLP
#Variables 4
#Binary Variables 0
#Integer Variables 2
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 2
Objective Sense min
Objective type polynomial
Objective curvature indefinite
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 3
#Linear Constraints 2
#Quadratic Constraints 0
#Polynomial Constraints 1
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 6
#Nonlinear Nonzeros in Jacobian 2
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#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 9.5400e-03
Maximal coefficient 3.1416e+00
Infeasibility of initial point 9.274e+05
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
*          4        1        1        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        3        0        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        5        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,x4,objvar;

Integer Variables  i1,i2;

Equations  e1,e2,e3,e4;


e1..  - 0.0625*i1 + 0.0193*x3 =L= 0;

e2..  - 0.0625*i2 + 0.00954*x3 =L= 0;

e3.. 3.1415927*(sqr(x3)*x4 + 1.33333333333333*POWER(x3,3)) =G= 1296000;

e4.. -(0.0389*i1*x3*x4 + 0.1111312*sqr(x3)*i2 + 0.012348046875*sqr(i1)*x4 + 
     0.0775*sqr(i1)*x3) + objvar =E= 0;

* set non-default bounds
i1.lo = 18; i1.up = 100;
i2.lo = 10; i2.up = 100;
x3.lo = 40; x3.up = 80;
x4.lo = 20; x4.up = 60;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


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