A Collective Neurodynamic Approach to Distributed Constrained Optimization

Abstract

This paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks (RNNs) for distributed constrained optimization. The objective function of the distributed optimization problems to be solved is a sum of local convex objective functions, which may be nonsmooth. Subject to its local constraints, each local objective function is minimized individually by using an RNN, with consensus among others. In contrast to existing continuous-time distributed optimization methods, the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems. Simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach. In addition, an application to the optimal placement problem is delineated to demonstrate the viability of the approach.

An Overview of Recent Advances in Event-Triggered Consensus of Multiagent Systems

“…Whether or not sampled-data of agent i should be broadcast or used at the sampling instant kh (k ∈ N) depends on when its ETC is violated. It is clear to know from (16) that, at the kth sampling instant, the event-triggered condition for agent i is closely related to the sampled-data error e i (kh) and the sampled-dataẑ i (kh) including the latest transmitted sampled-data x i (t i m h) of agent i and the latest transmitted sampled-data x j (t j m j h) of its neighbors. If the ETC in (16) is satisfied, the sampled-data of agent i is not needed to be transmitted to its neighbor agents.…”

“…If the ETC in (16) is satisfied, the sampled-data of agent i is not needed to be transmitted to its neighbor agents. It is worth mentioning that, when the ETC in (16) is always violated at each sampling time, it means that the sampled-data of agent i at each sampling time is required to be broadcasted. In this case, the event-triggered control scheme (16) is reduced to the standard periodic sampled-data one.…”

Distributed Continuous-Time Algorithms for Nonsmooth Extended Monotropic Optimization Problems

“…For example, it generalizes the optimization model in resource allocation problems [3], [14] by allowing nonsmooth objective functions and a more general equality constraint. Moreover, it covers the model proposed in [8] and generalizes the model in the distributed constrained optimal consensus problem [27] by allowing heterogeneous constraints.…”

“…Since x * = P Ω (y * ), it follows that (7) holds. By virtue of (7), (8) and Lemma 3.1, x * is the solution to problem (4).…”

Distributed continuous‐time algorithm for a general nonsmooth monotropic optimization problem

“…To date, although a wide spectrum of results have been reported for discrete-time networks with various scenarios in the literature, ranging from distributed optimization problems in the absence of constraints to those subject to constraints, [1][2][3][4][5] continuous-time algorithms have attracted an increasing interest in recent years mostly due to the fact that a lot of physical systems operate in a continuum domain, such as the current flow in smart grid. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] For instance, distributed convex optimization problems have been studied in the work of Yang et al 17 subject to local feasible constraints, local inequality and equality constraints, where a proportional-integral continuous-time algorithm has been designed with output information exchange.…”