New descent LQP alternating direction methods for solving a class of structured variational inequalities

Fixexd point theory and applications

Qamrul Hasan Ansari³  Suliman Al-Homidan⁴  Abdellah Bnouhachem⁵ 

[1] Minerals, Dhahran, Saudi Arabia;Statistics, King Fahd University of Petroleum &Department of Mathematics &ENSA, Ibn Zohr University, Agadir, Morocco;School of Management Science and Engineering, Nanjing University, Nanjing, P.R. China

关键词: structured variational inequalities;    logarithmic-quadratic proximal method;    projection method;    alternating direction method;    49J30;    47H09;    47J20;    49J40;   

DOI  :  10.1186/s13663-015-0387-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose two descent alternating direction methods based on a logarithmic-quadratic proximal method for structured variational inequalities. The first method can be viewed as an extension of the method proposed by Bnouhachem and Xu (Comput. Math. Appl. 67:671-680, 2014) by performing an additional step at each iteration. The second method generates the new iterate by searching the optimal step size along a new descent direction, which can be viewed as a refinement and improvement of the first one. Under certain conditions, the global convergence of the both methods is proved.

【 授权许可】

CC BY