# Compact R Implementation of Hooke and Jeeves Pattern Search Optimization The purpose of `hjn` is to minimize an unconstrained or bounds (box) and mask constrained function of several parameters by a Hooke and Jeeves pattern search. This didactic code is entirely in R to allow users to explore and understand the method. It also allows bounds (or box) constraints and masks (equality constraints) to be imposed on parameters. UTF-8 ```r hjn(par, fn, lower=-Inf, upper=Inf, bdmsk=NULL, control = list(trace=0), ...) ``` ## Arguments - `par`: A numeric vector of starting estimates. - `fn`: A function that returns the value of the objective at the supplied set of parameters `par` using auxiliary data in `...`. The first argument of `fn` must be `par`. - `lower`: A vector of lower bounds on the parameters. - `upper`: A vector of upper bounds on the parameters. - `bdmsk`: An indicator vector, having 1 for each parameter that is "free" or unconstrained, and 0 for any parameter that is fixed or MASKED for the duration of the optimization. - `control`: An optional list of control settings. - ``...``: Further arguments to be passed to `fn`. ## Details Functions `fn` must return a numeric value. The `control` argument is a list. - **maxfeval**: A limit on the number of function evaluations used in the search. - **trace**: Set 0 (default) for no output, >0 for trace output (larger values imply more output). - **eps**: Tolerance used to calculate numerical gradients. Default is 1.0E-7. See source code for `hjn` for details of application. - **`dowarn`**: = TRUE if we want warnings generated by optimx. Default is TRUE. - **`tol`**: Tolerance used in testing the size of the pattern search step. Note that the control `maximize` should NOT be used. ## Returns A list with components: - **par**: The best set of parameters found. - **value**: The value of the objective at the best set of parameters found. - **counts**: A two-element integer vector giving the number of calls to 'fn' and 'gr' respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to 'fn' to compute a finite-difference approximation to the gradient. - **convergence**: An integer code. '0' indicates successful convergence. '1' indicates that the function evaluation count 'maxfeval' was reached. - **message**: A character string giving any additional information returned by the optimizer, or 'NULL'. ## References Nash JC (1979). Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation. Adam Hilger, Bristol. Second Edition, 1990, Bristol: Institute of Physics Publications. ## See Also `optim` ## Examples ```r ##################### ## Rosenbrock Banana function fr <- function(x) { x1 <- x[1] x2 <- x[2] 100 * (x2 - x1 * x1)^2 + (1 - x1)^2 } ansrosenbrock0 <- hjn(fn=fr, par=c(1,2), control=list(maxfeval=2000, trace=0)) print(ansrosenbrock0) # use print to allow copy to separate file that # can be called using source() ##################### genrose.f<- function(x, gs=NULL){ # objective function ## One generalization of the Rosenbrock banana valley function (n parameters) n <- length(x) if(is.null(gs)) { gs=100.0 } fval<-1.0 + sum (gs*(x[1:(n-1)]^2 - x[2:n])^2 + (x[2:n] - 1)^2) return(fval) } xx<-rep(pi,10) lower<-NULL upper<-NULL bdmsk<-NULL cat("timings B vs U\n") lo<-rep(-100,10) up<-rep(100,10) bdmsk<-rep(1,10) tb<-system.time(ab<-hjn(xx,genrose.f, lower=lo, upper=up, bdmsk=bdmsk, control=list(trace=0, maxfeval=2000)))[1] tu<-system.time(au<-hjn(xx,genrose.f, control=list(maxfeval=2000, trace=0)))[1] cat("times U=",tu," B=",tb,"\n") cat("solution hjnu\n") print(au) cat("solution hjnb\n") print(ab) cat("diff fu-fb=",au$value-ab$value,"\n") cat("max abs parameter diff = ", max(abs(au$par-ab$par)),"\n") ######### One dimension test sqtst<-function(xx) { res<-sum((xx-2)*(xx-2)) } nn<-1 startx<-rep(0,nn) onepar<-hjn(startx,sqtst,control=list(trace=1)) print(onepar) ```

hjn function