Non-monotonous accelerated parallel subgradient projection algorithm for convex feasibility problem

The usual projection methods for solving convex feasibility problem (CFP) may lead to slow convergence for some starting points due to the 'tunnelling effect', which is connected with the monotone behaviour of the sequence and the exact orthogonal projection used in algorithms. To overcome...

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Bibliographic Details
Published in:Optimization Vol. 63; no. 4; pp. 571 - 584
Main Authors: Dang, Yazheng, Gao, Yan
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.04.2014
Taylor & Francis LLC
Subjects:
Algorithms
Construction
Convergence
Convex analysis
convex feasibility problem
Feasibility
Geometry
Mathematical problems
non-monotonous technique
nonsmoothness
Numerical analysis
Optimization
Projection
Studies
subgradient
Tunnelling
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:The usual projection methods for solving convex feasibility problem (CFP) may lead to slow convergence for some starting points due to the 'tunnelling effect', which is connected with the monotone behaviour of the sequence and the exact orthogonal projection used in algorithms. To overcome the effect, in this article, we apply the non-monotonous technique to the subgradient projection algorithm, instead of the exact orthogonal projection algorithm, to construct a non-monotonous parallel subgradient projection algorithm for solving CFP. Under some mild conditions, the convergence is shown. Preliminary numerical experiments also show that the proposed algorithm converges faster than that of the monotonous algorithm.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2012.677447