Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment

M. E. Abbasov ()
Additional contact information
M. E. Abbasov: Saint-Petersburg University, St. Petersburg State University, SPbSU, SPbU

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 18, 666-674

Abstract: Abstract Second-order methods play an important role in the theory of optimization. Due to the usage of more information about considered function, they give an opportunity to find the stationary point faster than first-order methods. Well-known and sufficiently studied Newton’s method is widely used to optimize smooth functions. The aim of this work is to obtain a second-order method for unconstrained minimization of nonsmooth functions allowing convex quadratic approximation of the augment. This method is based on the notion of coexhausters—new objects in nonsmooth analysis, introduced by V. F. Demyanov. First, we describe and prove the second-order necessary condition for a minimum. Then, we build an algorithm based on that condition and prove its convergence. At the end of the paper, a numerical example illustrating implementation of the algorithm is given.

Keywords: Nonsmooth analysis; Nondifferentiable optimization; Coexhausters; 49J52; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0796-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:joptap:v:171:y:2016:i:2:d:10.1007_s10957-015-0796-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-015-0796-7

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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