Primal-Dual Nonlinear Rescaling Method for Convex Optimization

R. Polyak and I. Griva
Additional contact information
R. Polyak: George Mason University
I. Griva: George Mason University

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 1, No 6, 156 pages

Abstract: Abstract In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge to zero with linear rate. Moreover, for any given ratio 0 > γ > 1, there is a fixed scaling parameter kγ > 0 such that each PDNR step shrinks the primal-dual error bound by at least a factor 0 > γ > 1, for any k ≥ kγ. The PDNR solver was tested on a variety of NLP problems including the constrained optimization problems (COPS) set. The results obtained show that the PDNR solver is numerically stable and produces results with high accuracy. Moreover, for most of the problems solved, the number of Newton steps is practically independent of the problem size.

Keywords: Nonlinear rescaling; duality; Lagrangian; primal-dual methods; multipliers methods (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://link.springer.com/10.1023/B:JOTA.0000041733.24606.99 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:122:y:2004:i:1:d:10.1023_b:jota.0000041733.24606.99

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

DOI: 10.1023/B:JOTA.0000041733.24606.99

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 ().