期刊
MATHEMATICAL PROGRAMMING
卷 170, 期 1, 页码 177-206出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-018-1303-3
关键词
Firmly nonexpansive operator; Monotone operator; Operator splitting; Proximal algorithm; Proximity operator; Proximity-preserving transformation; Self-dual class; Subdifferential
类别
资金
- National Science Foundation [CCF-1715671]
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized. We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents. In particular, we study new transformations which map proximity operators to proximity operators, and establish connections with self-dual classes of firmly nonexpansive operators. In addition, new insights and developments are proposed on the algorithmic front.
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