A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem. (27th March 2013)

• Record Type: Journal Article
• Authors: Gui, Zhuqing; Hu, Chunyan; Zhu, Zhibin
• Other Names: Bein W. Academic Editor.; Piunovskiy A. Academic Editor.; Silva G. Academic Editor.
• Is Part Of: ISRN operations research. Volume 2013(2013)
• Publication Date: 2013-03-27
• Subjects: Operations research -- Periodicals; Operations research; Electronic journals; Periodicals; 003
• DOI: 10.1155/2013/230717
• Languages: English
• ISSNs: 2314-6397

Abstract

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.