Table of Contents
ISRN Operations Research
Volume 2013 (2013), Article ID 230717, 9 pages
http://dx.doi.org/10.1155/2013/230717
Research Article

A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem

1School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
2School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China

Received 30 January 2013; Accepted 19 February 2013

Academic Editors: W. Bein, A. Piunovskiy, and G. Silva

Copyright © 2013 Zhuqing Gui et al. 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

Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm.