Select a search method for Newton-based optimizers

Specification

Alias: none

Argument(s): none

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Required (Choose One)	Group 1	value_based_line_search	Use only function values for line search
		gradient_based_line_search	Set the search method to use the gradient
		trust_region	Use trust region as the globalization strategy.
		tr_pds	Use direct search as the local search in a trust region method

Description

The search_method control is defined for all Newton-based optimizers and is used to select between trust_region, gradient_based_line_search, and value_based_line_search methods. The gradient_based_line_search option uses the line search method proposed by[61]. This option satisfies sufficient decrease and curvature conditions; whereas, value_base_line_search only satisfies the sufficient decrease condition. At each line search iteration, the gradient_based_line_search method computes the function and gradient at the trial point. Consequently, given expensive function evaluations, the value_based_line_search method is preferred to the gradient_based_line_search method. Each of these Newton methods additionally supports the tr_pds selection for unconstrained problems. This option performs a robust trust region search using pattern search techniques. Use of a line search is the default for bound-constrained and generally-constrained problems, and use of a trust_region search method is the default for unconstrained problems.