MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance oaer

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1.92309851 p1 ( gdx sol ) (infeas: 3e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.92309929 (ANTIGONE) -1.92309852 (BARON) -1.92309851 (COUENNE) -1.9231 (LINDO) -1.92309852 (SCIP) -1.92309902 (SHOT)
Referencesⓘ	Floudas, C A, Nonlinear and Mixed Integer Optimization: Fundamentals and Applications, Oxford University Press, 1995.
Sourceⓘ	MINOPT Model Library model oaer_test.dat
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	9
#Binary Variablesⓘ	3
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	9
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	7
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	2
Operands in Gen. Nonlin. Functionsⓘ	log
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	16
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
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ⓘ	9.0000e-01
Maximal coefficientⓘ	1.1000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        4        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         10        7        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         26       24        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,b7,b8,b9,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6;

Binary Variables  b7,b8,b9;

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


e1..  - 1.8*x1 - 1.8*x2 - 7*x3 - x4 - 1.2*x5 + 11*x6 - 3.5*b7 - b8 - 1.5*b9
      + objvar =E= 0;

e2.. -log(1 + x1) + x4 =E= 0;

e3.. -1.2*log(1 + x2) + x5 =E= 0;

e4..  - 0.9*x3 - 0.9*x4 - 0.9*x5 + x6 =E= 0;

e5..    x6 - b7 =L= 0;

e6..    x4 - 1.111111*b8 =L= 0;

e7..    x5 - 1.111111*b9 =L= 0;

e8..    b8 + b9 =L= 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;