Inertial Subgradient Projection Algorithms Extended to Equilibrium Problems

Author(s):  
Tran Van Thang
Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Junlong Zhu ◽  
Ping Xie ◽  
Mingchuan Zhang ◽  
Ruijuan Zheng ◽  
Ling Xing ◽  
...  

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.


2009 ◽  
Vol 14 (3) ◽  
pp. 335-351 ◽  
Author(s):  
Xiaolong Qin ◽  
Yeol Je Cho ◽  
Shin Min Kang

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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