Two-stage continuous-time triggered algorithms for constrained distributed optimization over directed graphs

Abstract

This paper proposes two-stage continuous-time triggered algorithms for solving distributed optimization problems with inequality constraints over directed graphs. The inequality constraints are penalized by adopting log-barrier penalty method. The first stage of the proposed algorithms is capable of finding the optimal point of each local optimization problem in finite time. In the second stage of the proposed algorithms, zero-gradient-sum algorithms with time-triggered and event-triggered communication strategies are considered in order to reduce communication costs. Then, with the help of LaSalle’s invariance principle, it is proved that the state solution of each agent reaches consensus at the optimal point of the considered penalty distributed optimization problem, and Zeno behavior is also excluded. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithms.