In this paper, we consider distributed optimization problems over a multiagent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of nonconvex problems and under the challenging setting, where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies, such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.
Bibliographical noteFunding Information:
Manuscript received September 19, 2017; revised March 1, 2018 and September 18, 2018; accepted November 23, 2018. Date of publication January 30, 2019; date of current version September 25, 2019. This work was supported in part by the National Science Foundation under Grant CMMI-1727757 and Grant CCF-1526078 and in part by the Air Force Office of Scientific Research under Grant 15RT0767. Recommended by Associate Editor U. V. Shanbhag. (Corresponding author: Mingyi Hong.) D. Hajinezhad is with the SAS Institute, Cary, NC 27513 USA (e-mail:, email@example.com).
- Distributed optimization
- Nonconvex optimization
- Primal-dual algorithms
- Zeroth-order information