Line search for generalized alternating projections

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

This paper is about line search for the generalized alternating projections (GAP) method. This method is a generalization of the von Neumann alternating projections method, where instead of alternating projections, relaxed projections are alternated. The method can be interpreted as an averaged iteration of a nonexpansive mapping. Therefore, a recently proposed line search method for such algorithms is applicable to GAP. We evaluate this line search and show situations when the line search can be performed with little additional cost. We also present a variation of the basic line search for GAP - The projected line search. We prove its convergence and show that the line search condition is convex in the step length parameter. We show that almost all convex optimization problems can be solved using this approach and numerical results show superior performance with both the standard and the projected line search, sometimes by several orders of magnitude, compared to the nominal method.

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Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics
Original languageEnglish
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4637-4642
Number of pages6
ISBN (Electronic)9781509059928
StatePublished - 2017 Jun 29
Peer-reviewedYes
Event2017 American Control Conference, ACC 2017 - Seattle, United States

Conference

Conference2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period2017/05/242017/05/26