An Adaptive Continuous-Time Algorithm for Nonsmooth Convex Resource Allocation Optimization

This article develops a novel continuous-time algorithm based on the idea of adaptive strategy for solving a resource allocation optimization with nonsmooth objective functions and constraints over multiagent network. It is proved that the state solution is globally bounded and finally converges to an optimal solution to the nonsmooth convex resource allocation problem. Compared with the existing algorithms, the strong/strict convexity of the objective function is relaxed and only convexity is required. Moreover, by employing an exact penalty approach for the distributed optimization, the primal-dual variables is avoided to introduce. Therefore, the proposed algorithm has a simple structure with low dimensionality of state variables. To show the effectiveness and practicability of the presented algorithm, a numerical example and an application in power system are presented.

Automated summary

This article introduces a novel continuous-time algorithm based on adaptive strategy for solving resource allocation optimization with nonsmooth objective functions and constraints over multiagent networks. The algorithm relaxes the strong/strict convexity of the objective function and only requires convexity, proving that the solution is globally bounded and converges to the optimal solution. By implementing an exact penalty approach for distributed optimization, it eliminates the need to introduce primal-dual variables, resulting in a simple structure with low dimensionality of state variables.