# General-purpose optimization - sequential application of methods Multiple minimization methods are applied in sequence to a single problem, with the output parameters of one method being used to start the next. UTF-8 ```r polyopt(par, fn, gr=NULL, lower=-Inf, upper=Inf, methcontrol=NULL, hessian=FALSE, control=list(), ...) ``` ## Arguments - `par`: a vector of initial values for the parameters for which optimal values are to be found. Names on the elements of this vector are preserved and used in the results data frame. - `fn`: A function to be minimized (or maximized), with first argument the vector of parameters over which minimization is to take place. It should return a scalar result. - `gr`: A function to return (as a vector) the gradient for those methods that can use this information. If 'gr' is `NULL`, a finite-difference approximation will be used. An open question concerns whether the SAME approximation code used for all methods, or whether there are differences that could/should be examined? - `lower, upper`: Bounds on the variables for methods such as `"L-BFGS-B"` that can handle box (or bounds) constraints. - `methcontrol`: An data frame of which each row gives an optimization method, a maximum number of iterations and a maximum number of function evaluations allowed for that method. Each method will be executed in turn until either the maximum iterations or function evaluations are completed, whichever is first. The next method is then executed starting with the best parameters found so far, else the function exits. - `hessian`: A logical control that if TRUE forces the computation of an approximation to the Hessian at the final set of parameters. If FALSE (default), the hessian is calculated if needed to provide the KKT optimality tests (see `kkt` in Details for the `control` list). This setting is provided primarily for compatibility with optim(). - `control`: A list of control parameters. See Details . - ``...``: For `optimx` further arguments to be passed to `fn` and `gr`; otherwise, further arguments are not used. ## Details Note that arguments after `...` must be matched exactly. See `optimr()` for other details. Note that this function does not (yet?) make use of a hess function to compute the hessian. ## Returns An array with one row per method. Each row contains: - **par**: The best set of parameters found for the method in question. - **value**: The value of ‘fn’ corresponding to ‘par’. - **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 completion - **message**: A character string giving any additional information returned by the optimizer, or ‘NULL’. - **hessian**: Always NULL for this routine. ## Source See the manual pages for `optim()` and the packages the DESCRIPTION `suggests`. ## Examples ```r fnR <- function (x, gs=100.0) { n <- length(x) x1 <- x[2:n] x2 <- x[1:(n - 1)] sum(gs * (x1 - x2^2)^2 + (1 - x2)^2) } grR <- function (x, gs=100.0) { n <- length(x) g <- rep(NA, n) g[1] <- 2 * (x[1] - 1) + 4*gs * x[1] * (x[1]^2 - x[2]) if (n > 2) { ii <- 2:(n - 1) g[ii] <- 2 * (x[ii] - 1) + 4 * gs * x[ii] * (x[ii]^2 - x[ii + 1]) + 2 * gs * (x[ii] - x[ii - 1]^2) } g[n] <- 2 * gs * (x[n] - x[n - 1]^2) g } x0 <- rep(pi, 4) mc <- data.frame(method=c("Nelder-Mead","Rvmmin"), maxit=c(1000, 100), maxfeval= c(1000, 1000)) ans <- polyopt(x0, fnR, grR, methcontrol=mc, control=list(trace=0)) ans mc <- data.frame(method=c("Nelder-Mead","Rvmmin"), maxit=c(100, 100), maxfeval= c(100, 1000)) ans <- polyopt(x0, fnR, grR, methcontrol=mc, control=list(trace=0)) ans mc <- data.frame(method=c("Nelder-Mead","Rvmmin"), maxit=c(10, 100), maxfeval= c(10, 1000)) ans <- polyopt(x0, fnR, grR, methcontrol=mc, control=list(trace=0)) ans ```

polyopt function