Title:

A nonderivative version of the gradient sampling algorithm for nonsmooth nonconvex optimization

Subtitle:

Raport Badawczy = Research Report ; RB/35/2009

Creator:

Kiwiel, Krzysztof

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2009

Description:

12 pages ; 21 cm ; Bibliography p. 11-12

Subject and Keywords:

Nonsmooth optimization ; Gradient sampling ; Generalized gradient ; Nonconvex ; Subgradient ; Gradient uogólniony ; Optymalizacja niegładka ; Próbkowanie gradientowe ; Niewypukły ; Funkcje uśrednione ; Averaged functions

Abstract:

The article gives a nonderivative version of the gradient sampling algorithm of Burke, Lewis and Overton for minimizing a locally Lipschitz function f on Rn that is continuously differentiable on an open dense subset. Instead of gradients of f, estimates of gradients of the Steklov averages of f were used. It has been shown that the nonderivative version retains the convergence properties of the gradient sampling algorithm. In particular, with probability 1 it either drives the f-values to -∞ or each of its cluster points is Clarke stationary for f.

Relation:

Raport Badawczy = Research Report

Resource type:

Text

Detailed Resource Type:

Report

Source:

RB-2009-35

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open