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

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A Correction to this article was published on 24 September 2020

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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 \({\mathcal {O}}(1/\sqrt{N})\) 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 \({\mathcal {O}}(1/N)\).

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Change history

  • 24 September 2020

    This erratum is published as due to some technical error author names appeared reversed in the final publication.

Notes

  1. http://plato.la.asu.edu/ftp/sipampl.pdf.

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Funding

Funding was provided by Singapore A*STAR (Grant No. 1421200078)

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Authors and Affiliations

  1. Institute of Operations Research and Analytics, National University of Singapore, Singapore, 119007, Singapore

    Bo Wei

  2. Krannert School of Management, Purdue University, West Lafayette, 47906, USA

    William B. Haskell

  3. Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai, 200030, China

    Sixiang Zhao

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  1. Bo Wei
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  2. William B. Haskell
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  3. Sixiang Zhao
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Correspondence to William B. Haskell.

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Wei, B., Haskell, W.B. & Zhao, S. The CoMirror algorithm with random constraint sampling for convex semi-infinite programming. Ann Oper Res 295, 809–841 (2020). https://doi.org/10.1007/s10479-020-03766-7

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