Accelerated Successive Convex Approximation for Nonlinear Optimization-Based Control

Abstract

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.