- Title
- Bregman monotone optimization algorithms
- Creator
- Bauschke, Heinz H.; Borwein, Jonathan M.; Combettes, Patrick L.
- Relation
- SIAM Journal on Control and Optimization Vol. 42, Issue 2, p. 596-636
- Publisher Link
- http://dx.doi.org/10.1137/S0363012902407120
- Publisher
- Society for Industrial and Applied Mathematics (SIAM)
- Resource Type
- journal article
- Date
- 2003
- Description
- A broad class of optimization algorithms based on Bregman distances in Banach spaces is unified around the notion of Bregman monotonicity. A systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate Bregman projection schemes. Another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of Bregman monotonicity and to include the operators commonly found in Bregman optimization methods. Special emphasis is placed on the viability of the algorithms and the importance of Legendre functions in this regard. Various applications are discussed.
- Subject
- Banach space; Fejér monotone; Bregman projection; Bregman monotone; B-class operator; convex feasibility problem; essentially smooth function; essentially strict convex function; Legendre function; monotone operator; proximal mapping; proximal point algorithm; resolvent; subgradient projection; block-iterative method; Bregman distance
- Identifier
- http://hdl.handle.net/1959.13/940298
- Identifier
- uon:12982
- Identifier
- ISSN:0363-0129
- Language
- eng
- Full Text
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