MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

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 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;