Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Non-smooth Approach

2020/01/02 by Li, Weijian, Zeng, Xianlin, Liang, Shu +1
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2001.00509

Abstract

We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact penalty method, we reformulate the problem equivalently as a standard distributed one without consensus constraints. Then we design a distributed projected subgradient algorithm with the help of differential inclusions. Furthermore, we show that the algorithm converges to the optimal solution exponentially for strongly convex objective functions.

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