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

In optimx: Expanded Replacement and Extension of the 'optim' Function

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(dowarn=TRUE), ...)

Arguments

par	A vector of values for the parameters which are supposedly optimal.
fn	The objective function
gr	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

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.

Note that evaluated Hessians are often not symmetric, and many, possibly most, examples will fail the is.Symmetric() function. In such cases, the check on the Hessian uses the mean of the Hessian and its transpose.

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. Sorting is a property of the eigen() function.
ngatend	The computed (unconstrained) gradient at the solution parameters.
nnatend	The computed (unconstrained) hessian at the solution parameters.

See Also

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)

# 2023-8-23 need dowarn specified or get error
# Note: may want to set control=list(dowarn=TRUE)
kkans <- kktchk(ans$par, jones, jonesg)
kkans

optimx documentation built on Oct. 24, 2023, 5:06 p.m.