Proximal minimization methods with generalized Bregman functions

We consider methods for minimizing a convex function f that generate a sequence {xk} by taking xk+1 to be an approximate minimizer of f(x)+Dh(x,xk)/ck, where ck > 0 and Dh is the D-function of a Bregman function h. Extensions are made to B-functions that generalize Bregman functions and cover mor...

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Bibliographic Details
Published in:SIAM journal on control and optimization 1997-07, Vol.35 (4), p.1142-1168
Main Author: KIWIEL, K. C
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Mathematical programming
Methods
Operational research and scientific management
Operational research. Management science
Optimization. Search problems
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Summary:We consider methods for minimizing a convex function f that generate a sequence {xk} by taking xk+1 to be an approximate minimizer of f(x)+Dh(x,xk)/ck, where ck > 0 and Dh is the D-function of a Bregman function h. Extensions are made to B-functions that generalize Bregman functions and cover more applications. Convergence is established under criteria amenable to implementation. Applications are made to nonquadratic multiplier methods for nonlinear programs.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012995281742