Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems

2012 ◽  
Vol 157 (3) ◽  
pp. 803-819 ◽  
Author(s):  
A. J. Zaslavski
Keyword(s):  
Approximate Solutions ◽  
Projection Algorithms ◽  
Convex Feasibility Problems ◽  
Subgradient Projection ◽  
Convex Feasibility

scholarly journals On Projection Algorithms for Solving Convex Feasibility Problems

SIAM Review ◽  
1996 ◽  
Vol 38 (3) ◽  
pp. 367-426 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Jonathan M. Borwein
Keyword(s):  
Projection Algorithms ◽  
Convex Feasibility Problems ◽  
Convex Feasibility

An Acceleration Scheme for Solving Convex Feasibility Problems Using Incomplete Projection Algorithms

2004 ◽  
Vol 35 (2-4) ◽  
pp. 331-350 ◽  
Author(s):  
N. Echebest ◽  
M.T. Guardarucci ◽  
H. Scolnik ◽  
M.C. Vacchino
Keyword(s):  
Projection Algorithms ◽  
Convex Feasibility Problems ◽  
Convex Feasibility

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.

Iterative approaches to convex feasibility problems in Banach spaces

2006 ◽  
Vol 64 (9) ◽  
pp. 2022-2042 ◽  
Author(s):  
John G. O’Hara ◽  
Paranjothi Pillay ◽  
Hong-Kun Xu
Keyword(s):  
Banach Spaces ◽  
Convex Feasibility Problems ◽  
Convex Feasibility
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