MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance alan

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	2.92500000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	2.92500000 (ALPHAECP) 2.92500000 (ANTIGONE) 2.92500000 (BARON) 2.92500000 (BONMIN) 2.92500000 (COUENNE) 2.92500000 (CPLEX) 2.92500000 (GUROBI) 2.92500000 (LINDO) 2.92500000 (SCIP) 2.92500000 (SHOT)
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
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.2000e+01
Infeasibility of initial pointⓘ	0.5048
Sparsity Jacobianⓘ
Sparsity 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;