A Finite-Time Consensus Continuous-Time Algorithm for Distributed Pseudoconvex Optimization With Local Constraints

In this article, we develop a continuous-time algorithm based on a multiagent system for solving distributed, nonsmooth, and pseudoconvex optimization problems with local convex inequality constraints. The proposed algorithm is modeled by differential inclusion, which is based on the penalty method rather than the projection method. Compared with existing methods, the proposed algorithm has the following advantages. First, this algorithm can solve the distributed optimization problem, in which the global objective function is pseudoconvex and the local objective functions are subdifferentially regular in the global feasible region; Moreover, each agent can have different constraints. Second, this algorithm does not require exact penalty parameters or projection operators. Third, the subgradient gains for different agents may be nonuniform. Fourth, all agents reach a consensus in finite time. It is proven that under certain assumptions, from an arbitrary initial state, the solutions of all the agents will enter their local inequality feasible region and remain there, reach consensus in finite time, and converge to the optimal solution set of the primal distributed optimization problem. Numerical experiments show that the proposed algorithm is effective.