Gradient-free distributed optimization and nash equilibrium seeking

Abstract

With the prevalence of multi-agent system concept, there is a strong interest to investigate the optimization and game problems among multiple agents or decision-makers. With the increase of the data size, computational burden and network complexity, solving these problems in a distributed manner has found great advantages in terms of the efficiency and reliability compared to the traditional centralized methods. However, most distributed algorithms need to rely on the gradient information of the cost functions, which is rather restrictive, especially for the problems where such information is not available. This dissertation focuses on the research of gradient-free distributed algorithms in optimization problems where the agents collaboratively achieve a system-level objective, and Nash equilibrium seeking problems where the agents/players selfishly minimize their own cost functions. Effectiveness of all proposed algorithms is verified through both theoretical analysis and numerical simulations.