Exponentially Convergent Algorithms Design for Distributed Resource Allocation Under Non-Strongly Convex Condition: From Continuous-Time to Event-Triggered Communication

The standard condition for achieving exponential convergence of distributed resource allocation is the strongly convex objective functions, which is hard to be guaranteed in many practical cyber-physical systems. To study the resource allocation problem in a more general setting, we provide a new condition which only requires that the gradient-based map satisfies the metric subregularity. This condition is weaker than the standard strongly convex condition and is imposed to the objective functions. Based on such a relaxed condition, two new kinds of distributed allocation algorithms are proposed under continuous-time and event-triggered communications, respectively. The exponential convergence of our proposed algorithms are verified by rigorous theoretical analyses and some economic dispatch examples in the industrial cyber-physical system.