Iterative Subgradient Projection Algorithm

2021 ◽  
pp. 217-242
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Projection Algorithm ◽  
Subgradient Projection ◽  
Subgradient Projection Algorithm

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.

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