kktchk: Check Kuhn Karush Tucker conditions for a supposed function minimum

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

par

A vector of values for the parameters which are supposedly optimal.

The objective function

The gradient function

hess

The Hessian function

upper

Upper bounds on the parameters

lower

Lower bounds on the parameters

maximize

Logical TRUE if function is being maximized. Default FALSE.

control

A list of controls for the function

...

The dot arguments needed for evaluating the function and gradient and hessian

Value

The output is a list consisting of

gmax

The absolute value of the largest gradient component in magnitude.

evratio

The ratio of the smallest to largest Hessian eigenvalue. Note that this may be negative.

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.

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.

hev

The calculated hessian eigenvalues, sorted largest to smallest??

ngatend

The computed (unconstrained) gradient at the solution parameters.

nnatend

The computed (unconstrained) hessian at the solution parameters.

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.

Examples

Run this code

# NOT RUN {
cat("Show how kktc works\n")

# require(optimx)
require(optextras)

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



# }