Gradient Approximation and Multivariable Derivative-Free Optimization Based on Noncommutative Maps

• 成果类型: Article
• 署名作者: Feiling, Jan; Belabbas, Mohamed-Ali; Ebenbauer, Christian
• 署名单位: University of Stuttgart; University of Illinois System; University of Illinois Urbana-Champaign; RWTH Aachen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3129741
• 发表日期: 2022
• 页码: 6381-6396
• 关键词: adaptive control; extremum seeking; non-holonomic systems; optimization; optimization algorithms; Perturbation methods

摘要

In this article, multivariable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multivariable objective functions based on noncommutative maps is introduced. The procedure is based on the construction of an exploration sequence to specify where the objective function is evaluated and the definition of so-called gradient generating functions which are composed with the objective function, such that the procedure mimics a gradient descent algorithm. Various theoretical properties of the proposed class of algorithms are investigated and numerical examples are presented.