fminnewton.m

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Finds a local minimum (or maximum) of a function of several variables, based on fminlbfgs.m code from D. Kroon, University of Twente (Nov 2010).

Syntax

    [x,fx,grad,hess,data]=fminnewton(cost_function,x_0,optim,hess_init,cost_fun_vars)

Description

This is the most developed optimisation algorithm within Spinach. It uses a line search

The cost_function is a function handle to that which produces as cost, gradient, and\or Hessian as a function of an initial guess, x_0. optim is an optional argument containing the optimisation options as a pair-wise cell structure.

Arguments

    cost_function     - Function handle, e.g. @cost_function, 
    
    x_0               - Initial guess for the waveform.
    
    optim             - Structure providing the options for the numerical optimisation algorithm.
                        See optim_tols.m for all options.
                          
    hess_init         - (optional) an initial Hessian to use for quasi-newton methods.
                        If not provided, the identity is used as a default.
                          
    cost_fun_vars     - (optional) an set of variable to pass to the cost function.
                        These can be modified within the cost function.

Returns

    x              - Output waveform at the end of the optimisation.
                     Should be the waveform at a local minimum (or maximum) cost.
    
    fx             - Output cost at the end of the optimisation.
    
    grad           - Output gradient at the end of the optimisation.
    
    hess           - Output Hessian matrix at the end of the optimisation.
                     Has meaning from 'bfgs', 'sr1', or 'newton', returns the identity otherwise.
    
    data           - data structure containing diagnostics of the optimisation algorithm.

Notes

This function is coded both for minimisation (default) and maximisation. This option is defined in the optim structure from optim_tols.m.

See also

linesearch.m, optim_tols.m, hessreg.m, hessprep.m


Version 1.9, authors: David Goodwin