R: Perform axial search around a supposed minimum and provide...

axsearch {optextras} | R Documentation

## Perform axial search around a supposed minimum and provide diagnostics

### Description

Nonlinear optimization problems often terminate at points in the parameter space that are not satisfactory optima. This routine conducts an axial search, stepping forward and backward along each parameter and computing the objective function. This allows us to compute the `tilt` and `radius of curvature` or `roc` along that parameter axis.

`axsearch` assumes that one is MINIMIZING the function `fn`. While we believe that it will work using the wrapper `ufn` from this package with the 'maximize=TRUE' setting, we believe it is much safer to write your own function that is to be minimized. That is minimize (-1)*(function to be maximized). All discussion here is in terms of minimization.

Axial search may find parameters with a function value lower than that at the supposed minimum, i.e., lower than `fmin`.

In this case `axsearch` exits immediately with the new function value and parameters. This can be used to restart an optimizer, as in the optimx wrapper.

### Usage

           axsearch(par, fn=NULL, fmin=NULL, lower=NULL, upper=NULL, bdmsk=NULL, trace=0, ...)

### Arguments

`par` | A numeric vector of values of the optimization function parameters that are at a supposed minimum.
`fn` | The user objective function
`fmin` | The value of the objective function at the parameters `par`. ?? what if fmin==NULL?
`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` | If trace>0, then local output is enabled.
`...` | Extra arguments for the user function.

### Details

None.

### Value

A list with components:

`bestfn` | The lowest (best) function value found (??maximize??) during the axial search, else the original fmin value. (This is actively set in that case.)
`par` | The vector of parameters at the best function value.
`details` | A data frame reporting the original parameters, the forward step and backward step function values, the size of the step taken for a particular parameter, the tilt and the roc (radius of curvature). Some elements will be NA if we find a lower function value during the axial search.

### Examples

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[Package optextras version 2016-8.8 Index]