Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11326
Title: Using simplex gradients of nonsmooth functions in direct search methods
Authors: Custódio, A. L. 
Dennis Jr., John E. 
Vicente, Luís Nunes 
Keywords: Derivative free optimization; Simplex gradients; Poisedness; Nonsmooth analysis; Generalized pattern search methods; Mesh adaptive direct search
Issue Date: 2006
Publisher: Centro de Matemática da Universidade de Coimbra
Keywords: Derivative free optimization; Simplex gradients; Poisedness; Nonsmooth analysis; Generalized pattern search methods; Mesh adaptive direct search
Issue Date: 2006
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 06-48 (2006)
Abstract: It has been shown recently that the efficiency of direct search methods that use opportunistic polling in positive spanning directions can be improved significantly by reordering the poll directions according to descent indicators built from simplex gradients. The purpose of this paper is twofold. First, we analyze the properties of simplex gradients of nonsmooth functions in the context of direct search methods like the Generalized Pattern Search (GPS) and the Mesh Adaptive Direct Search (MADS), for which there exists a convergence analysis in the nonsmooth setting. Our analysis does not require continuous differentiability and can be seen as an extension of the accuracy properties of simplex gradients known for smooth functions. Secondly, we test the use of simplex gradients when pattern search is applied to nonsmooth functions, confirming the merit of the poll ordering strategy for such problems.
URI: http://hdl.handle.net/10316/11326
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

Files in This Item:
File Description SizeFormat
Using simplex gradients of nonsmooth functions.pdf172.09 kBAdobe PDFView/Open
Show full item record

Page view(s) 50

246
checked on Aug 20, 2019

Download(s)

49
checked on Aug 20, 2019

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.