# bmstep: Compute the maximum step along a search direction. In optextras: Tools to Support Optimization Possibly with Bounds and Masks

## Description

Nonlinear optimization problems often have explicit or implicit upper and lower bounds on the parameters of the function to be miminized or maximized. These are called bounds or box constraints. Some of the parameters may be fixed for a given problem or for a temporary trial. These fixed, or masked, paramters are held at one value during a specific 'run' of the optimization.

The bmstep() function computes the maximum step possible (which could be infinite) along a particular search direction from current parameters to bounds.

## Usage

 `1` ``` bmstep(par, srchdirn, lower=NULL, upper=NULL, bdmsk=NULL, trace=0) ```

## Arguments

 `par` A numeric vector of starting values of the optimization function parameters. `srchdirn` A numeric vector giving the search direction. `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. Partly for historical reasons, we use the same array during the progress of optimization as an indicator that a parameter is at a lower bound (bdmsk element set to -3) or upper bound (-1). `trace` An integer that controls whether diagnostic information is displayed. A positive value displays information, 0 (default) does not.

## Details

The bmstep function will compute and return (as a double or Inf) the maximum step to the bounds.

## Value

A double precision value or Inf giving the maximum step to the bounds.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```##################### xx <- c(1, 1) lo <- c(0, 0) up <- c(100, 40) sdir <- c(4,1) bm <- c(1,1) # both free ans <- bmstep(xx, sdir, lo, up, bm, trace=1) # stepsize print(ans) # distance print(ans*sdir) # New parameters print(xx+ans*sdir) ```

optextras documentation built on Dec. 31, 2019, 3:01 a.m.