A derivative-free approximate gradient sampling algorithm for finite minimax problems

W. Hare () and J. Nutini

Computational Optimization and Applications, 2013, vol. 56, issue 1, 38 pages

Abstract: In this paper we present a derivative-free optimization algorithm for finite minimax problems. The algorithm calculates an approximate gradient for each of the active functions of the finite max function and uses these to generate an approximate subdifferential. The negative projection of 0 onto this set is used as a descent direction in an Armijo-like line search. We also present a robust version of the algorithm, which uses the ‘almost active’ functions of the finite max function in the calculation of the approximate subdifferential. Convergence results are presented for both algorithms, showing that either f(x k )→−∞ or every cluster point is a Clarke stationary point. Theoretical and numerical results are presented for three specific approximate gradients: the simplex gradient, the centered simplex gradient and the Gupal estimate of the gradient of the Steklov averaged function. A performance comparison is made between the regular and robust algorithms, the three approximate gradients, and a regular and robust stopping condition. Copyright Springer Science+Business Media New York 2013

Keywords: Derivative-free optimization; Minimax problems; Generalized gradient; Subgradient approximation (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-013-9547-6 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:56:y:2013:i:1:p:1-38

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-013-9547-6

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().