An Adaptive Accelerated Derivative-Free Optimization Algorithm Based on Noncommutative Maps

• 成果类型: Article
• 署名作者: Chu, Minghui; Huo, Xin; Ebenbauer, Christian; Ma, Kemao
• 署名单位: Harbin Institute of Technology; RWTH Aachen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3641250
• 发表日期: 2026
• 关键词: EXTREMUM-SEEKING CONTROL; Random search; STABILITY; approximation

摘要

In this article, an adaptive accelerated derivative-free optimization algorithm is developed. A composition of noncommutative maps based on objective function evaluations is used to approximate an accelerated gradient descent algorithm with a momentum term. An adaptive step-size rule and an adaptive momentum term are introduced to improve the algorithm's performance in terms of convergence speed and steady-state accuracy. Semi-global asymptotic stability of the proposed algorithm is proved for a class of convex objective functions under suitable assumptions. Simulation results are shown and compared to other derivative-free optimization algorithms.