Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints

Daniel D. Selvaratnam; Iman Shames; Jonathan H. Manton; Mohammad Zamani

doi:10.1109/CDC.2018.8619392

Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints

Daniel D. Selvaratnam, Iman Shames, Jonathan H. Manton, Mohammad Zamani

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and suboptimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	849-854
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619392
Publication status	Published - 2 Jul 2018
Externally published	Yes
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Access to Document

10.1109/CDC.2018.8619392

Cite this

Selvaratnam, D. D., Shames, I., Manton, J. H., & Zamani, M. (2018). Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 849-854). Article 8619392 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619392

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title = "Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints",

abstract = "This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and suboptimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.",

author = "Selvaratnam, {Daniel D.} and Iman Shames and Manton, {Jonathan H.} and Mohammad Zamani",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2018",

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doi = "10.1109/CDC.2018.8619392",

language = "English",

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Selvaratnam, DD, Shames, I, Manton, JH & Zamani, M 2018, Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619392, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 849-854, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619392

Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints. / Selvaratnam, Daniel D.; Shames, Iman; Manton, Jonathan H. et al.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 849-854 8619392 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and suboptimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.

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DO - 10.1109/CDC.2018.8619392

M3 - Conference contribution

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BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

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ER -

Selvaratnam DD, Shames I, Manton JH, Zamani M. Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 849-854. 8619392. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2018.8619392

Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints

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