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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: alan

Formats ams gms lp mod nl osil pip
Primal Bounds
2.92500000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
2.92500000 (ALPHAECP)
2.92500000 (ANTIGONE)
2.92500000 (BARON)
2.92500000 (BONMIN)
2.92500000 (COUENNE)
2.92500000 (LINDO)
2.92500000 (SCIP)
References Manne, Alan S, GAMS/MINOS: Three examples, Tech. Rep., Department of Operations Research, Stanford University, 1986.
Source GAMS Model Library model alan
Application Portfolio Optimization
Added to library 01 May 2001
Problem type MBQP
#Variables 8
#Binary Variables 4
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 3
#Constraints 7
#Linear Constraints 7
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 20
#Nonlinear Nonzeros in Jacobian 0
#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 0.5048
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
*          9        5        4        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         24       21        3        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar,b6,b7,b8,b9;

Positive Variables  x1,x2,x3,x4;

Binary Variables  b6,b7,b8,b9;

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


e1..    x1 + x2 + x3 + x4 =E= 1;

e2..    8*x1 + 9*x2 + 12*x3 + 7*x4 =E= 10;

e3.. x1*(4*x1 + 3*x2 - x3) + x2*(3*x1 + 6*x2 + x3) + x3*(x2 - x1 + 10*x3)
      - objvar =E= 0;

e4..    x1 - b6 =L= 0;

e5..    x2 - b7 =L= 0;

e6..    x3 - b8 =L= 0;

e7..    x4 - b9 =L= 0;

e8..    b6 + b7 + b8 + b9 =L= 3;

* set non-default levels
x1.l = 0.302884615384618;
x2.l = 0.0865384615384593;
x3.l = 0.504807692307693;
x4.l = 0.10576923076923;
objvar.l = 2.89903846153846;

* set non-default marginals
e1.m = 1;
e2.m = 1;
e3.m = 1;
x1.m = 1;
x2.m = 1;

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: 2018-09-14 Git hash: ac5a5314
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