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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e40

Formats ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
30.41421350 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
30.41421347 (ANTIGONE)
30.41421347 (BARON)
30.41421350 (COUENNE)
30.41421300 (LINDO)
30.41421350 (SCIP)
28.24264050 (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.
Shin, Dong Ku, Gürdal, Z, and Griffin, O H, A penalty approach for nonlinear optimization with discrete design variables, Engineering Optimization, 16:1, 1990, 29-42.
Source BARON book instance misc/e40
Added to library 01 Sep 2002
Problem type MINLP
#Variables 4
#Binary Variables 0
#Integer Variables 3
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 3
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 0
#Constraints 8
#Linear Constraints 4
#Quadratic Constraints 1
#Polynomial Constraints 3
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 19
#Nonlinear Nonzeros in Jacobian 6
#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
Minimal coefficient 1.3190e-01
Maximal coefficient 1.2000e+01
Infeasibility of initial point 3.462
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        5        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        2        0        3        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         23       17        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,x4,objvar;

Integer Variables  i1,i2,i3;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9;


e1.. (-0.15*i1*i2) - 0.14142135*i2*i3 - 0.1319*i1*i3 + x4 =E= 0;

e2..    1.7317*i2 + 1.03366*i3 - x4 =L= 0;

e3..    0.634*i1 + 2.828*i3 - x4 =L= 0;

e4..    0.5*i1 - 2*i2 - x4 =L= 0;

e5..  - 0.5*i1 + 2*i2 - x4 =L= 0;

e6.. (-1 + i1)*(-2 + i1)*(-3 + i1)*(-5 + i1)*(-8 + i1)*(-10 + i1)*(-12 + i1)
      =E= 0;

e7.. (-1 + i2)*(-2 + i2)*(-3 + i2)*(-5 + i2)*(-8 + i2)*(-10 + i2)*(-12 + i2)
      =E= 0;

e8.. (-1 + i3)*(-2 + i3)*(-3 + i3)*(-5 + i3)*(-8 + i3)*(-10 + i3)*(-12 + i3)
      =E= 0;

e9..  - 2*i1 - i2 - 1.4142135*i3 + objvar =E= 0;

* set non-default bounds
i1.lo = 1; i1.up = 12;
i2.lo = 1; i2.up = 12;
i3.lo = 1; i3.up = 12;

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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