A self-adaptive descent LQP alternating direction method for the structured variational inequalities

被引：0
作者：
Abdellah Bnouhachem
机构：
[1] Ibn Zohr University,Equipe MAISI
来源：
Numerical Algorithms | 2021年 / 86卷
关键词：
Variational inequalities; Monotone operator; Logarithmic-quadratic proximal method; Projection method; Alternating direction method; 49J40; 65N30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, by combining the logarithmic-quadratic proximal (LQP) method and alternating direction method, we proposed an LQP alternating direction method for solving structured variational inequalities. The new iterate is generated by searching the optimal step size along a descent direction with a new step size αk. The choice of the descent direction and the step size selection strategies are important for the algorithm’s efficiency. The O(1/t) convergence rate of the proposed method is studied, and its efficiency is also verified by some numerical experiments.
引用
收藏
页码：303 / 324
页数：21
相关论文
共 79 条
[1]  
Auslender A(1999)A logarithmic-quadratic proximal method for variational inequalities Comput. Optim. Appl. 12 31-40
[2]  
Teboulle M(2001)Entropic proximal decomposition methods for convex programs and variational inequalities Math. Program. 91 33-47
[3]  
Ben-Tiba S(2004)Interior gradient and epsilon-subgradient descent methods for constrained convex minimization Math. Oper. Res. 29 1-26
[4]  
Auslender A(2006)Interior gradient and proximal methods for convex and conic optimization SIAM J. Optim. 16 697-725
[5]  
Teboulle M(2000)Lagrangian duality and related multiplier methods for variational inequality problems SIAM J. Optim. 10 1097-1115
[6]  
Auslender A(2013)An inexact alternating direction method for solving a class of structured variational inequalities Appl. Math. Comput. 219 7837-7846
[7]  
Teboulle M(2014)On LQP alternating direction method for solving variational inequality problems with separable structure J. Inequal. Appl. 2014 1-15
[8]  
Auslender A(2014)An inexact LQP alternating direction method for solving a class of structured variational inequalities Comput. Math. Appl. 67 671-680
[9]  
Teboulle M(2014)A descent LQP alternating direction method for solving variational inequality problems with separable structure Appl. Math. Comput. 246 519-532
[10]  
Auslender A(2014)Parallel LQP alternating direction method for solving variational inequality problems with separable structure J. Inequal. Appl. 2014 1-14
12345678