The Proximal Point Algorithm Revisited

Yunda Dong ()
Additional contact information
Yunda Dong: Zhengzhou University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 2, No 8, 478-489

Abstract: Abstract In this paper, we consider the proximal point algorithm for the problem of finding zeros of any given maximal monotone operator in an infinite-dimensional Hilbert space. For the usual distance between the origin and the operator’s value at each iterate, we put forth a new idea to achieve a new result on the speed at which the distance sequence tends to zero globally, provided that the problem’s solution set is nonempty and the sequence of squares of the regularization parameters is nonsummable. We show that it is comparable to a classical result of Brézis and Lions in general and becomes better whenever the proximal point algorithm does converge strongly. Furthermore, we also reveal its similarity to Güler’s classical results in the context of convex minimization in the sense of strictly convex quadratic functions, and we discuss an application to an ϵ-approximation solution of the problem above.

Keywords: Monotone operator; Convex minimization; Proximal point algorithm; Rate of convergence (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0351-3 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:161:y:2014:i:2:d:10.1007_s10957-013-0351-3

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

DOI: 10.1007/s10957-013-0351-3

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 ().