Anderson Accelerated Feasible Sequential Linear Programming

TL;DR

This paper introduces an accelerated version of Feasible Sequential Linear Programming using Anderson Acceleration, significantly improving convergence speed and reducing computational effort in solving constrained optimization problems.

Contribution

The paper presents AA(d)-FSLP, an enhanced FSLP algorithm that incorporates Anderson Acceleration to improve convergence and efficiency in constrained optimization.

Findings

AA(d)-FSLP achieves faster convergence than standard FSLP.

The method reduces the number of constraint evaluations needed.

Successful application demonstrated on a robot motion planning problem.

Abstract

This paper proposes an accelerated version of Feasible Sequential Linear Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in all intermediate iterates by means of an iterative update strategy which is based on repeated evaluation of zero-order information. This technique was successfully applied to techniques such as Model Predictive Control and Moving Horizon Estimation, but it can exhibit slow convergence. Moreover, keeping all iterates feasible in FSLP entails a large number of additional constraint evaluations. In this paper, Anderson Acceleration (AA($d$)) is applied to the zero-order update strategy improving the convergence rate and therefore decreasing the number of constraint evaluations in the inner iterative procedure of the FSLP algorithm. AA($d$) achieves an improved contraction rate in the inner iterations, with proven local linear convergence. In addition, it is observed that due to the improved zero-order update strategy, AA($d$)-FSLP takes larger steps to find an optimal solution, yielding faster overall convergence. The performance of AA($d$)-FSLP is examined for a time-optimal point-to-point motion problem of a parallel SCARA robot. The reduction of the number of constraint evaluations and overall iterations compared to FSLP is successfully demonstrated.