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

Abstract

This paper investigates a general monotropic optimization problem for continuous-time networks, where the global objective function is a sum of local objective functions that are only known to individual agent, and general constraints are taken into account, including local inequality constraints, global equality constraint, and local feasible constraints. In addition, all functions involved in the objective functions and inequality constraints are not necessarily differentiable. To solve the problem, a distributed continuous-time algorithm is designed using subgradient projections, and it is shown that the proposed algorithm is well defined in the sense that the existence of its solutions can be guaranteed. Furthermore, it is proved that the algorithm converges to an optimal solution for the general monotropic optimization problem. Finally, a simulation example is provided for validating the theoretical result.