On a Proximal Point Method for Optimization in Banach Spaces

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On a Proximal Point Method for Optimization in Banach Spaces

Show simple item record Iusem, Alfredo N. en Butnariu, Dan en 2010-06-03T18:22:18Z en 2010-06-03T18:22:18Z en 1997-02 en
dc.identifier.uri en
dc.description.abstract We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;318 en
dc.subject Proximal point method en
dc.subject Bochner integral en
dc.subject Bregman distance en
dc.subject Convex optimization problem en
dc.subject Uniformly convex Banach space en
dc.subject Totally convex function en
dc.subject.lcsh Banach spaces en
dc.subject.lcsh Mathematics Research en
dc.title On a Proximal Point Method for Optimization in Banach Spaces en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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