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

作者：Bnouhachem Abdellah; Al Homidan Suliman^*; Ansari Qamrul Hasan

来源：Fixed Point Theory and Applications, 2015, 2015(1): 137.

DOI：10.1186/s13663-015-0387-1

• structured variational inequalities
• logarithmic-quadratic proximal method
• projection method
• alternating direction method

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.

• 出版日期2015-8-7
• 单位南京大学; 中国石油大学（北京）