Inertial Subgradient Projection Algorithms Extended to Equilibrium Problems

2021 ◽  
Author(s):  
Tran Van Thang
Keyword(s):  
Equilibrium Problems ◽  
Projection Algorithms ◽  
Subgradient Projection

scholarly journals Distributed Stochastic Subgradient Projection Algorithms Based on Weight-Balancing over Time-Varying Directed Graphs

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Junlong Zhu ◽  
Ping Xie ◽  
Mingchuan Zhang ◽  
Ruijuan Zheng ◽  
Ling Xing ◽  
...  
Keyword(s):  
Directed Graphs ◽  
Stochastic Matrix ◽  
Projection Algorithm ◽  
Time Varying ◽  
Projection Algorithms ◽  
Doubly Stochastic ◽  
Subgradient Projection ◽  
Subgradient Projection Algorithm ◽  
Theoretical Results ◽  
Over Time

We consider a distributed constrained optimization problem over graphs, where cost function of each agent is private. Moreover, we assume that the graphs are time-varying and directed. In order to address such problem, a fully decentralized stochastic subgradient projection algorithm is proposed over time-varying directed graphs. However, since the graphs are directed, the weight matrix may not be a doubly stochastic matrix. Therefore, we overcome this difficulty by using weight-balancing technique. By choosing appropriate step-sizes, we show that iterations of all agents asymptotically converge to some optimal solutions. Further, by our analysis, convergence rate of our proposed algorithm is O(ln Γ/Γ) under local strong convexity, where Γ is the number of iterations. In addition, under local convexity, we prove that our proposed algorithm can converge with rate O(ln Γ/Γ). In addition, we verify the theoretical results through simulations.

CONVERGENCE ANALYSIS ON HYBRID PROJECTION ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

2009 ◽  
Vol 14 (3) ◽  
pp. 335-351 ◽  
Author(s):  
Xiaolong Qin ◽  
Yeol Je Cho ◽  
Shin Min Kang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Variational Inequality Problems ◽  
Fixed Point Problems ◽  
Projection Algorithms

In this paper, we consider an iterative method for equilibrium problems, fixed point problems and variational inequality problems in the framework of Banach space. The results presented in this paper improve and extend the corresponding results announced by many others.

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