We study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step-sizes. This algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the Bregman distances to the members of the family of convex sets. The resulting algorithm is a new steered sequential Bregman projection method which generates sequences that converge if they are bounded, regardless of whether the convex feasibility problem is or is not consistent. For orthogonal projections and affine sets the boundedness condition is always fulfilled.
|Number of pages||21|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|State||Published - Nov 2004|
Bibliographical noteFunding Information:
We are grateful to Professor Ron Aharoni from the Department of Mathematics at the Technion—Israel Institute of Technology in Haifa for his collaboration and insightful contributions throughout this research. We thank a referee whose illuminating comments helped to improve this paper. The work of M. Zaknoon on this research is part of his Ph.D. thesis  . The research of Y. Censor on the topic of this paper is partially supported by grant No. 592/00 of the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities and by NIH grant No. HL70472. The work of A.R. De Pierro was supported by CNPq grant No. 300969/2003-1 and FAPESP grant No. 2002/07153-2.
ASJC Scopus subject areas
- Applied Mathematics