SQP alternating direction method with a new optimal step size for solving variational inequality problems with separable structure

Applicable Analysis and Discrete Mathematics

article

Abdellah Bnouhachem¹  Themistocles M.Rassias² 

[1] School of Management Science and Engineering, Nanjing University, Nanjing, 210093, P.R. China. Ibn Zohr University;Department of Mathematics, National Technical University of Athens Zografou Campus 157 80

关键词: Variational inequalities;    logarithmic-quadratic proximal method;    square-quadratic proximal method;    projection method;    alternating direction method.;   

DOI  :  10.2298/AADM1801224B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In this paper, we suggest and analyze a new alternating direction scheme forthe separable constrained convex programming problem. The theme of thispaper is twofold. First, we consider the square-quadratic proximal (SQP)method. Next, by combining the alternating direction method with SQPmethod, we propose a descent SQP alternating direction method by using thesame descent direction as in [6] with a new step size αk. Under appropriateconditions, the global convergence of the proposed method is proved. Weshow the O(1/t) convergence rate for the SQP alternating direction method.Some preliminary computational results are given to illustrate the efficiencyof the proposed method.

【 授权许可】

Unknown