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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: st_e29

Formats ams gms mod nl osil
Primal Bounds (infeas ≤ 1e-08)
-0.94347050 p1 ( gdx sol )
(infeas: 6e-15)
Other points (infeas > 1e-08)  
Dual Bounds
-0.94347050 (ANTIGONE)
-0.94347050 (BARON)
-0.94347050 (COUENNE)
-0.94347050 (LINDO)
-0.94347055 (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.
Ashrafi, Noushin and Berman, Oded, Optimization models for selection of programs, considering cost and reliability, IEEE Transactions on Reliability, 41:2, 1992, 281-287.
Source BARON book instance misc/e29
Added to library 01 Sep 2002
Problem type MBNLP
#Variables 11
#Binary Variables 8
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type polynomial
Objective curvature indefinite
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 3
#Constraints 7
#Linear Constraints 4
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 3
Operands in Gen. Nonlin. Functions log
Constraints curvature indefinite
#Nonzeros in Jacobian 27
#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 1
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        3        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12        4        8        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31       25        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,b4,b5,b6,b7,b8,b9,b10,b11,objvar;

Positive Variables  x1,x2,x3;

Binary Variables  b4,b5,b6,b7,b8,b9,b10,b11;

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


e1.. x1*x2*x3 + objvar =E= 0;

e2.. -log(1 - x1) - 2.30258509299405*b4 - 1.6094379124341*b5
      - 1.89711998488588*b6 =E= 0;

e3.. -log(1 - x2) - 2.99573227355399*b7 - 1.6094379124341*b8
      - 1.89711998488588*b9 =E= 0;

e4.. -log(1 - x3) - 3.91202300542815*b10 - 2.81341071676004*b11 =L= 0;

e5..  - b4 - b5 - b6 =L= -1;

e6..  - b7 - b8 - b9 =L= -1;

e7..  - b10 - b11 =L= -1;

e8..    3*b4 + b5 + 2*b6 + 3*b7 + 2*b8 + b9 + 3*b10 + 2*b11 =L= 10;

* set non-default bounds
x1.up = 0.997;
x2.up = 0.9985;
x3.up = 0.9988;

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: 2019-07-12 Git hash: 46a7b4f1
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