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(dowarn=TRUE), ...)

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.

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.

Examples

Run this code

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