International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2347-2357
doi:10.1155/IJMMS.2005.2347

Descent methods for convex optimization problems in Banach spaces

Abstract

We consider optimization problems in Banach spaces, whose cost functions are convex and smooth, but do not possess strengthened convexity properties. We propose a general class of iterative methods, which are based on combining descent and regularization approaches and provide strong convergence of iteration sequences to a solution of the initial problem.