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% File src/library/stats/man/kktchk.Rd
% Part of the R package, http://www.R-project.org
% Copyright 1995-2007 R Core Development Team
% Distributed under GPL 2 or later
\name{kktchk}
\alias{kktchk}
\encoding{UTF-8}
\title{Check Kuhn Karush Tucker conditions for a supposed function minimum}
\concept{minimization}
\concept{maximization}
\description{
Provide a check on Kuhn-Karush-Tucker conditions based on quantities
already computed. Some of these used only for reporting.
}
\usage{
kktchk(par, fn, gr, hess=NULL, upper=NULL, lower=NULL,
maximize=FALSE, control=list(), ...)
}
\arguments{
\item{par}{A vector of values for the parameters which are supposedly optimal.}
\item{fn}{The objective function}
\item{gr}{The gradient function}
\item{hess}{The Hessian function}
\item{upper}{Upper bounds on the parameters}
\item{lower}{Lower bounds on the parameters}
\item{maximize}{Logical TRUE if function is being maximized. Default FALSE.}
\item{control}{A list of controls for the function}
\item{...}{The dot arguments needed for evaluating the function and gradient and hessian}
}
\details{
kktchk computes the gradient and Hessian measures for BOTH unconstrained and
bounds (and masks) constrained parameters, but the kkt measures are evaluated
only for the constrained case.
}
\value{
The output is a list consisting of
\item{gmax}{The absolute value of the largest gradient component in magnitude.}
\item{evratio}{The ratio of the smallest to largest Hessian eigenvalue. Note that this
may be negative.}
\item{kkt1}{A logical value that is TRUE if we consider the first (i.e., gradient)
KKT condition to be satisfied. WARNING: The decision is dependent on tolerances and
scaling that may be inappropriate for some problems.}
\item{kkt2}{A logical value that is TRUE if we consider the second (i.e., positive
definite Hessian) KKT condition to be satisfied. WARNING: The decision is dependent
on tolerances and scaling that may be inappropriate for some problems.}
\item{hev}{The calculated hessian eigenvalues, sorted largest to smallest??}
\item{ngatend}{The computed (unconstrained) gradient at the solution parameters.}
\item{nnatend}{The computed (unconstrained) hessian at the solution parameters.}
}
\seealso{
\code{\link{optim}}
}
\examples{
cat("Show how kktc works\n")
# require(optimx)
jones<-function(xx){
x<-xx[1]
y<-xx[2]
ff<-sin(x*x/2 - y*y/4)*cos(2*x-exp(y))
ff<- -ff
}
jonesg <- function(xx) {
x<-xx[1]
y<-xx[2]
gx <- cos(x * x/2 - y * y/4) * ((x + x)/2) * cos(2 * x - exp(y)) -
sin(x * x/2 - y * y/4) * (sin(2 * x - exp(y)) * 2)
gy <- sin(x * x/2 - y * y/4) * (sin(2 * x - exp(y)) * exp(y)) - cos(x *
x/2 - y * y/4) * ((y + y)/4) * cos(2 * x - exp(y))
gg <- - c(gx, gy)
}
ans <- list() # to ensure structure available
# If optimx package available, the following can be run.
# xx<-0.5*c(pi,pi)
# ans <- optimr(xx, jones, jonesg, method="Rvmmin")
# ans
ans$par <- c(3.154083, -3.689620)
kkans <- kktchk(ans$par, jones, jonesg)
kkans
}
\keyword{nonlinear}
\keyword{optimize}
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