Accelerated Successive Convex Approximation for Nonlinear Optimization-Based Control

• 成果类型: Article
• 署名作者: Wu, Jinxian; Dai, Li; Dou, Songshi; Xia, Yuanqing
• 署名单位: Beijing Institute of Technology; University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3555375
• 发表日期: 2025
• 页码: 6237-6244
• 关键词: convergence; vectors; COSTS; cost function; Nonlinear equations; Newton method; Collision avoidance; iterative methods; indexes; Hands; Fixed-point problem; nonlinear control; Successive convex approximation (SCA)

摘要

The successive convex approximation (SCA) methods stand out as the viable option for nonlinear optimization-based control, as it effectively addresses the challenges posed by nonlinear (potentially nonconvex) optimization problems by transforming them into a sequence of strongly convex subproblems. However, the current SCA algorithm exhibits a slow convergence rate, resulting in a relatively poor performance within a limited sample time. In this article, the process of SCA is retreated as solving a fixed-point nonlinear equation. By analyzing the derivative properties of this nonlinear equation, we introduce a Newton-based accelerated SCA algorithm designed to enhance the local convergence rate while inheriting all favorable characteristics of the SCA methods. Specifically, our algorithm offers the following benefits: first, it is capable of effectively tackling nonlinear optimization-based control problems; second, it permits flexible termination with all generated intermediate solutions being feasible for the original nonlinear problem; third, it guarantees convergence with locally superlinear convergence rate to the stationary point of the original nonlinear problem. Finally, we conduct experiments in a multiagent collision avoidance scenario to show its validity.