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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 492305, 13 pages
http://dx.doi.org/10.1155/2013/492305
Research Article

A General Self-Adaptive Relaxed-PPA Method for Convex Programming with Linear Constraints

Institute of Systems Engineering, Southeast University, Nanjing 210096, China

Received 27 June 2013; Accepted 21 July 2013

Academic Editor: Abdellah Bnouhachem

Copyright © 2013 Xiaoling Fu. 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.

Abstract

We present an efficient method for solving linearly constrained convex programming. Our algorithmic framework employs an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA). In particular, the stepsize choice condition of our algorithm is weaker than some elegant PPA-type methods. This condition is flexible and effective. Self-adaptive strategies are proposed to improve the convergence in practice. We theoretically show under mild conditions that our method converges in a global sense. Finally, we discuss applications and perform numerical experiments which confirm the efficiency of the proposed method. Comparisons of our method with some state-of-the-art algorithms are also provided.