A Novel Continuous-Time Algorithm for Nonsmooth Convex Resource Allocation Optimization

Changsen Fu, Lei Xue, Wenwen Jia, Sitian Qin

Keywords: Continuous-time algorithm, multi-agent network, resource allocation, distributed nonsmooth optimization.

Abstract: This paper develops a novel continuous-time algorithm modeled by a differential inclusion for solving a resource allocation optimization with nonsmooth objective functions and constraints over multi-agent network. It is proved that the state solution of the proposed algorithm enters feasible region of resource allocation problem in finite time and lies in the feasible region after that. Furthermore, it is shown that the state solution is global bounded and finally converges to an optimal solution to the nonsmooth convex resource allocation problem. Compared with the existing algorithms, the continuous-time algorithm proposed in this paper does not rely on the strong convexity or strict convexity of objective functions and has a simple structure with a low amount of state variables. Moreover, the algorithm avoids employing the projection operator. To show the effectiveness and practicability of the presented algorithm, numerical simulations and an application in power system are presented.

Submission Number: 7