MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_testgr1

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-12.81160000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-12.81160000 (ALPHAECP)
-12.81160000 (ANTIGONE)
-12.81160000 (BARON)
-12.81160000 (BONMIN)
-12.81160000 (COUENNE)
-12.81160000 (CPLEX)
-12.81160000 (GUROBI)
-12.81160000 (LINDO)
-12.81160000 (SCIP)
-12.81160000 (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.
Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne, 1999.
Source BARON book instance iqp/testgr1
Added to library 01 Sep 2002
Problem type IQP
#Variables 10
#Binary Variables 0
#Integer Variables 10
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 10
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 10
#Nonlinear Nonzeros in Objective 10
#Constraints 5
#Linear Constraints 5
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 41
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10
#Nonzeros in Diagonal of Hessian of Lagrangian 10
#Blocks in Hessian of Lagrangian 10
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.0000e-04
Maximal coefficient 9.0000e+00
Infeasibility of initial point 0
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
*          6        1        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11        1        0       10        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         52       42       10        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10;

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


e1..    8*i1 + 7*i2 + 9*i3 + 9*i5 + 8*i6 + 2*i7 + 4*i9 + i10 =L= 530;

e2..    3*i1 + 4*i2 + 6*i3 + 9*i4 + 6*i6 + 9*i7 + i8 + i10 =L= 395;

e3..    2*i2 + i3 + 5*i4 + 5*i5 + 7*i7 + 4*i8 + 2*i9 =L= 350;

e4..    5*i1 + 7*i3 + i4 + 7*i5 + 5*i6 + 7*i8 + 9*i9 + 5*i10 =L= 405;

e5..    i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 =L= 200;

e6.. -(0.00055*i1*i1 - 0.0583*i1 + 0.0019*i2*i2 + 0.2318*i2 + 0.0002*i3*i3 - 
     0.0108*i3 + 0.00095*i4*i4 + 0.1634*i4 + 0.0046*i5*i5 - 0.138*i5 + 0.0035*
     i6*i6 + 0.357*i6 + 0.00315*i7*i7 - 0.1953*i7 + 0.00475*i8*i8 - 0.361*i8 + 
     0.0048*i9*i9 + 0.1824*i9 + 0.003*i10*i10 - 0.162*i10) + objvar =E= 0;

* set non-default bounds
i1.up = 100;
i2.up = 100;
i3.up = 100;
i4.up = 100;
i5.up = 100;
i6.up = 100;
i7.up = 100;
i8.up = 100;
i9.up = 100;
i10.up = 100;

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;


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