Fortified-Descent Simplicial Search Method: A General Approach (1995)
| Venue: | SIAM J. Optim |
| Citations: | 11 - 1 self |
BibTeX
@TECHREPORT{Tseng95fortified-descentsimplicial,
author = {Paul Tseng},
title = {Fortified-Descent Simplicial Search Method: A General Approach},
institution = {SIAM J. Optim},
year = {1995}
}
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Abstract
We propose a new simplex-based direct search method for unconstrained minimization of a realvalued function f of n variables. As in other methods of this kind, the intent is to iteratively improve an n-dimensional simplex through certain reflection/expansion/contraction steps. The method has three novel features. First, a user-chosen integer m k specifies the number of "good" vertices to be retained in constructing the initial trial simplices--reflected, then either expanded or contracted--at iteration k. Second, a trial simplex is accepted only when it satisfies the criteria of fortified descent, which are stronger than the criterion of strict descent used in most direct search methods. Third, the number of additional function evaluations needed to check a trial reflected/expanded simplex for fortified descent can be controlled. If one of the initial trial simplices satisfies the fortified descent criteria, it is accepted as the new simplex; otherwise, the simplex is shrunk a fracti...
