On the convergence of general projection methods for solving convex feasibility problems with applications to the inverse problem of image recovery. (2nd September 2018)

• Record Type: Journal Article
• Authors: Zhao, Xiaopeng; Köbis, Markus Arthur
• Is Part Of: Optimization. Volume 67:Number 9(2018)
• Page Start: 1409
• Page End: 1427
• Publication Date: 2018-09-02
• Subjects: Convex feasibility problem -- image recovery -- projection algorithm -- system of closed convex sets; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1474355
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: For an arbitrary family of closed convex sets with nonempty intersection in a Hilbert space, we consider the classical convex feasibility problem. We study the convergence property of the recently introduced unified projection algorithm B-EMOPP for solving this problem. For this, a new general control strategy is proposed, which we call the 'quasi-coercive control'. Under mild assumptions, we prove the convergence of B-EMOPP using these new control strategies as well as various other strategies. Several known results are extended and improved. The proposed algorithm is then applied to the inverse problem of image recovery.