# Check Kuhn Karush Tucker conditions for a supposed function minimum Provide a check on Kuhn-Karush-Tucker conditions based on quantities already computed. Some of these used only for reporting. UTF-8 ```r 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. - `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. ## Returns 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. ## See Also `optim` ## Examples ```r 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 ```

kktchk function