Anderson Acceleration for Linearly Converging SQP-Type Methods

TL;DR

This paper demonstrates that Anderson acceleration can enhance the local convergence of SQP-type methods in constrained optimization, with practical implementation and numerical validation in optimal control problems.

Contribution

It introduces the application of Anderson acceleration to SQP methods, including a heuristic for better convergence away from the solution, and provides implementation in acados with numerical results.

Findings

AA improves convergence speed of SQP methods in optimal control.

The heuristic helps maintain convergence efficiency farther from the solution.

Numerical examples show consistent improvements across different SQP variants.

Abstract

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a general family of (inexact) SQP-type methods can benefit from AA and introduce a simple heuristic to alleviate slower convergence farther from the solution. The method is implemented in the software framework acados. Numerical examples from optimal control illustrate consistent improvements in convergence of different SQP-type methods.