compl {GNE} | R Documentation |
Complementarity functions
Description
Classic Complementarity functions
Usage
phiFB(a, b)
GrAphiFB(a, b)
GrBphiFB(a, b)
phipFB(a, b, p)
GrAphipFB(a, b, p)
GrBphipFB(a, b, p)
phirFB(a, b)
GrAphirFB(a, b)
GrBphirFB(a, b)
phiMin(a, b)
GrAphiMin(a, b)
GrBphiMin(a, b)
phiMan(a, b, f, fprime)
GrAphiMan(a, b, f, fprime)
GrBphiMan(a, b, f, fprime)
phiKK(a, b, lambda)
GrAphiKK(a, b, lambda)
GrBphiKK(a, b, lambda)
phiLT(a, b, q)
GrAphiLT(a, b, q)
GrBphiLT(a, b, q)
compl.par(type=c("FB", "pFB", "rFB", "Min", "Man", "LT", "KK"),
p, f, fprime, q, lambda)
## S3 method for class 'compl.par'
print(x, ...)
## S3 method for class 'compl.par'
summary(object, ...)
Arguments
a |
first parameter. |
b |
second parameter. |
f , fprime |
a univariate function and its derivative. |
lambda |
a parameter in [0, 2[. |
q |
a parameter >1. |
p |
a parameter >0. |
type |
a character string for the complementarity
function type: either |
x , object |
an object of class |
... |
further arguments to pass to |
Details
We implement 5 complementarity functions From Facchinei & Pang (2003).
- (i)
phiFB
the Fischer-Burmeister complementarity function
\sqrt{a^2+b^2} - (a+b)
. The penalized version isphiFB(a,b) - p*max(a,0)*max(b,0)
, whereas the regularized version isphiFB(a,b) - epsilon
.- (ii)
phiMin
the minimum complementarity function
\min(a,b)
.- (iii)
phiMan
the Mangasarian's family of complementarity function
f(|a-b|) - f(a) - f(b)
, typicallyf(t)=t
orf(t)=t^3
.- (iv)
phiKK
the Kanzow-Kleinmichel complementarity function
(\sqrt( (a-b)^2 + 2*\lambda*a*b ) - (a+b) ) / (2-\lambda)
.- (v)
phiLT
the Luo-Tseng complementarity function
(a^q + b^q)^(1/q) - (a+b)
.
GrAXXX
and GrBXXX
implements the derivative of the complementarity
function XXX
with respect to a
and b
respectively.
compl.par
creates an object of class "compl.par"
with attributes
"type"
a character string and "fun","grA","grB"
the corresponding
functions for a given type.
Optional arguments are also available, e.g. lambda for the KK complementarity
function.
Value
A numeric or an object of class "compl.par"
.
Author(s)
Christophe Dutang
References
F. Facchinei and J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag (New York 2003).
See Also
See also GNE.nseq
.
Examples
phiFB(1, 2)
phiLT(1, 2, 2)
phiKK(1, 2, 1)
-2*phiMin(1, 2)
phiMan(1, 2, function(t) t)
complFB <- compl.par("FB")
summary(complFB)
complKK <- compl.par("KK", lambda=1)
summary(complKK)
complKK$fun(1, 1, complKK$lambda)
complFB$fun(1, 1)