Line search for generalized alternating projections

Mattias Fält, Pontus Giselsson

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Sammanfattning

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.

Originalspråkengelska
Titel på värdpublikation2017 American Control Conference, ACC 2017
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor4637-4642
Antal sidor6
ISBN (elektroniskt)9781509059928
DOI
StatusPublished - 2017 juni 29
Evenemang2017 American Control Conference, ACC 2017 - Seattle, USA
Varaktighet: 2017 maj 242017 maj 26

Konferens

Konferens2017 American Control Conference, ACC 2017
Land/TerritoriumUSA
OrtSeattle
Period2017/05/242017/05/26

Ämnesklassifikation (UKÄ)

  • Beräkningsmatematik

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