Open AccessA New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming
Author(s) -
Liang Fang
Publication year - 2019
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v16i0.8152
Subject(s) - smoothing , mathematics , continuation , interior point method , line search , convergence (economics) , algorithm , linear programming , range (aeronautics) , mathematical optimization , cone (formal languages) , function (biology) , second order cone programming , computer science , geometry , statistics , materials science , computer security , convex optimization , evolutionary biology , regular polygon , economics , composite material , biology , programming language , economic growth , radius
Second-order cone programming has received considerable attention in the past decades because of its wide range of applications. Non-interior continuation method is one of the most popular and efficient methods for solving second-order cone programming partially due to its superior numerical performances. In this paper, a new smoothing form of the well-known Fischer-Burmeister function is given. Based on the new smoothing function, an inexact non-interior continuation algorithm is proposed. Attractively, the new algorithm can start from an arbitrary point, and it solves only one system of linear equations inexactly and performs only one line search at each iteration. Moreover, under a mild assumption, the new algorithm has a globally linear and locally Q-quadratical convergence. Finally, some preliminary numerical results are reported which show the effectiveness of the presented algorithm.