A direct method for solving integral penalty transcriptions of optimal control problems
File(s)
Accepted version
Author(s)
Neuenhofen, Martin P
Kerrigan, Eric
Type
Conference Paper
Abstract
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of equality constrained optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM) for solving this class of problems. However, if the equality constraints of the discretization are inconsistent, then ALM might not converge to a point that minimizes the unconstrained bias of the objective and penalty term. Therefore, in this paper we explore a modification of ALM that fits our purpose. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem.
Date Issued
2021-01-11
Date Acceptance
2020-07-16
Citation
2020 59th IEEE Conference on Decision and Control (CDC), 2021, pp.4822-4827
Publisher
IEEE
Start Page
4822
End Page
4827
Journal / Book Title
2020 59th IEEE Conference on Decision and Control (CDC)
Copyright Statement
© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Source
IEEE Conference on Decision and Control
Publication Status
Published
Start Date
2020-12-14
Finish Date
2020-12-18
Coverage Spatial
South Korea
Date Publish Online
2021-01-11