Log-Sigmoid Multipliers Method in Constrained Optimization

Roman Polyak

Annals of Operations Research, 2001, vol. 101, issue 1, 427-460

Abstract: In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augmented Lagrangian techniques. We established convergence of the LS type penalty method under very mild assumptions on the input data and estimated the rate of convergence of the LS multipliers method under the standard second order optimality condition for both exact and nonexact minimization. Some important properties of the dual function and the dual problem, which are based on the LS Lagrangian, were discovered and the primal–dual LS method was introduced. Copyright Kluwer Academic Publishers 2001

Keywords: log-sigmoid; multipliers method; duality; smoothing technique (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1010938423538 (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:annopr:v:101:y:2001:i:1:p:427-460:10.1023/a:1010938423538

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1023/A:1010938423538

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().