The CoMirror algorithm with random constraint sampling for convex semi-infinite programming

Bo Wei, William B. Haskell () and Sixiang Zhao
Additional contact information
Bo Wei: National University of Singapore
William B. Haskell: Purdue University
Sixiang Zhao: Shanghai Jiao Tong University

Annals of Operations Research, 2020, vol. 295, issue 2, No 13, 809-841

Abstract: Abstract The CoMirror algorithm, by Beck et al. (Oper Res Lett 38(6):493–498, 2010), is designed to solve convex optimization problems with one functional constraint. At each iteration, it performs a mirror-descent update using either the subgradient of the objective function or the subgradient of the constraint function, depending on whether or not the constraint violation is below some tolerance. In this paper, we combine the CoMirror algorithm with inexact cut generation to create the SIP-CoM algorithm for solving semi-infinite programming (SIP) problems. First, we provide general error bounds for SIP-CoM. Then, we propose two specific random constraint sampling schemes to approximately solve the cut generation problem for generic SIP. When the objective and constraint functions are generally convex, randomized SIP-CoM achieves an $${\mathcal {O}}(1/\sqrt{N})$$ O ( 1 / N ) convergence rate in expectation (in terms of the optimality gap and SIP constraint violation). When the objective and constraint functions are all strongly convex, this rate can be improved to $${\mathcal {O}}(1/N)$$ O ( 1 / N ) .

Keywords: Semi-infinite programming; Random constraint sampling; Corporative stochastic approximation (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-020-03766-7 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:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03766-7

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

DOI: 10.1007/s10479-020-03766-7

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 ().