Accelerated Successive Convex Approximation for Nonlinear Optimization-Based Control

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 non-convex) 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 paper, 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 (ASCA) algorithm designed to enhance the local convergence rate while inheriting all favorable characteristics of the SCA methods. Specifically, our algorithm offers the following benefits: (i) It is capable of effectively tackling nonlinear optimization-based control problems; (ii) It permits flexible termination with all generated intermediate solutions being feasible for the original nonlinear problem; and (iii) It guarantees convergence with locally superlinear convergence rate to the stationary point of the original nonlinear problem. Finally, we conduct experiments in a multi-agent collision avoidance scenario to show its validity.