A Distributed Optimization Problem Subject to Partial-Impact Cost Functions

This article focuses on a distributed optimization problem subject to partial-impact cost functions that relates to two decision variable vectors. To this end, two algorithms are presented with the aim of solving the considered optimization problem in a structure fashion and in a gradient fashion, respectively. Furthermore, a connection between the equilibrium of the induced algorithm and the involved optimization problem is established, with the aid of the tools from nonsmooth analysis and change of coordinate theorem. Two numerical examples with practical significance are given to demonstrate the efficiency of the designed algorithm.