- Title
- Union averaged operators with applications to proximal algorithms for min-convex functions
- Creator
- Dao, Minh; Tam, Matthew
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185580
- Identifier
- vital:16699
- Identifier
-
https://doi.org/10.1007/s10957-018-1443-x
- Identifier
- ISBN:0022-3239
- Abstract
- In this paper, we introduce and study a class of structured set-valued operators, which we call union averaged nonexpansive . At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued averaged nonexpansive operators. We investigate various structural properties of the class and show, in particular, that is closed under taking unions, convex combinations, and compositions, and that their fixed point iterations are locally convergent around strong fixed points. We then systematically apply our results to analyze proximal algorithms in situations, where union averaged nonexpansive operators naturally arise. In particular, we consider the problem of minimizing the sum two functions, where the first is convex and the second can be expressed as the minimum of finitely many convex functions.
- Publisher
- New York: Springer US
- Relation
- Journal of optimization theory and applications Vol. 181, no. 1 (2018), p. 61-94
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Subject
- Algorithms; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Convex analysis; Engineering; Mathematics; Mathematics - Optimization and Control; Mathematics and Statistics; Operations Research/Decision Theory; Operators; Theory of Computation; 4901 Applied mathematics
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