On subgradient projectors
Heinz H. Bauschke, Caifang Wang, Xianfu Wang, Jia Xu
TL;DR
This paper systematically studies the subgradient projector in convex optimization, analyzing its key properties and discussing related operators, supported by numerous illustrative examples.
Contribution
It provides a comprehensive analysis of the subgradient projector's fundamental properties and explores the Yamagishi-Yamada operator, enhancing understanding in convex optimization methods.
Findings
Subgradient projector is continuous under certain conditions
It exhibits nonexpansiveness and monotonicity properties
The Yamagishi-Yamada operator is discussed in relation to subgradient projectors
Abstract
The subgradient projector is of considerable importance in convex optimization because it plays the key role in Polyak's seminal work - and the many papers it spawned - on subgradient projection algorithms for solving convex feasibility problems. In this paper, we offer a systematic study of the subgradient projector. Fundamental properties such as continuity, nonexpansiveness, and monotonicity are investigated. We also discuss the Yamagishi-Yamada operator. Numerous examples illustrate our results.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Digital Image Processing Techniques