Convergence rates of subgradient methods for quasi-convex optimization problems

Yaohua Hu (), Jiawen Li () and Carisa Kwok Wai Yu ()
Additional contact information
Yaohua Hu: Shenzhen University
Jiawen Li: Shenzhen University
Carisa Kwok Wai Yu: The Hang Seng University of Hong Kong

Computational Optimization and Applications, 2020, vol. 77, issue 1, No 7, 183-212

Abstract: Abstract Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we investigate the quantitative convergence theory, including the iteration complexity and convergence rates, of various subgradient methods for solving quasi-convex optimization problems in a unified framework. In particular, we consider a sequence satisfying a general (inexact) basic inequality, and investigate the global convergence theorem and the iteration complexity when using the constant, diminishing or dynamic stepsize rules. More importantly, we establish the linear (or sublinear) convergence rates of the sequence under an additional assumption of weak sharp minima of Hölderian order and upper bounded noise. These convergence theorems are applied to establish the iteration complexity and convergence rates of several subgradient methods, including the standard/inexact/conditional subgradient methods, for solving quasi-convex optimization problems under the assumptions of the Hölder condition and/or the weak sharp minima of Hölderian order.

Keywords: Quasi-convex programming; Subgradient method; Iteration complexity; Convergence rates; Primary: 65K05; 90C26; Secondary: 49M37 (search for similar items in EconPapers)
Date: 2020
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/s10589-020-00194-y 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:coopap:v:77:y:2020:i:1:d:10.1007_s10589-020-00194-y

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

DOI: 10.1007/s10589-020-00194-y

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 ().