On the Finite Convergence of a Projected Cutter Method

Heinz H. Bauschke (), Caifang Wang (), Xianfu Wang () and Jia Xu ()
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Heinz H. Bauschke: University of British Columbia
Caifang Wang: Shanghai Maritime University
Xianfu Wang: University of British Columbia
Jia Xu: University of British Columbia

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 3, No 12, 916 pages

Abstract: Abstract The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the fixed point set has nonempty interior. Our assumptions on the parameters are more general than existing ones. Various limiting examples and comparisons are provided.

Keywords: Convex function; Cutter; Fejér monotone sequence; Finite convergence; Quasi firmly nonexpansive mapping; Subgradient projector; 90C25; 47H04; 47H05; 47H09; 65K10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0659-7

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