Bregman-Legendre multidistance projection algorithms for convex feasibility and optimization (Q2768012)

This paper presents a new version of \textit{L. Bregman}'s successive generalized projection (SGP) algorithm [see e.g. Zh. Vychl. Mat. Mat. Fiz. 7, 620-631 (1967; Zbl 0186.23807)] for solving the convex feasibility problem (CFP): find a common point of some closed convex sets in the Euclidean space. NEWLINENEWLINENEWLINEThe so-called multidistance successive generalized projection (MSGP) algorithm proposed by the author extends the Bregman's (SGP) algorithm, this time generalized distances being induced by appropriate Bregman-Legendre functions [see e.g. \textit{H. H. Bauschke} and \textit{J. M. Borwein}, SIAM Rev. 38, No. 3, 367-426 (1996; Zbl 0865.47039)] that may vary with the convex sets involved in (CFP). In order to ensure the convergence of the (MSGP) algorithm, some additional assumptions are imposed by the use of a dominating generalized distance induced by a super-coercive Bregman-Legendre function. NEWLINENEWLINENEWLINETwo applications of the general (MSGP) algorithm are presented: an iterative solution procedure for the split feasibility problem, and an interior point algorithm for iterative optimization.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00058].