International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2347-2357

Descent methods for convex optimization problems in Banach spaces

M. S. S. Ali

Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

Received 3 November 2004; Revised 22 July 2005

Copyright © 2005 M. S. S. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.