Robust Optimization via Discrete-Time Saddle Point Algorithm

Keivan Ebrahimi; Umesh Vaidya; Nicola Elia

doi:10.1109/CDC40024.2019.9028953

Robust Optimization via Discrete-Time Saddle Point Algorithm

Keivan Ebrahimi
, Umesh Vaidya
, Nicola Elia

Electrical and Computer Engineering

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

3 Scopus citations

Abstract

We discover discrete-time counterpart of the continuous-time saddle point algorithm developed in [1] for solving robust optimization problems. Under the assumption that the cost function is convex in the decision variable and uncertainties enter concavely in the robust optimization problem, we prove global asymptotic convergence of the saddle-point algorithm to the robust optimal solution. The sub-gradient nature of the proposed discrete-time algorithm allows us to handle robust optimization problems with discontinuous cost function and constraint.

Original language	English (US)
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2473-2478
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9028953
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: Dec 11 2019 → Dec 13 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	12/11/19 → 12/13/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Publisher link

10.1109/CDC40024.2019.9028953

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Ebrahimi, K., Vaidya, U., & Elia, N. (2019). Robust Optimization via Discrete-Time Saddle Point Algorithm. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 2473-2478). Article 9028953 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9028953

Robust Optimization via Discrete-Time Saddle Point Algorithm. / Ebrahimi, Keivan; Vaidya, Umesh; Elia, Nicola.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2473-2478 9028953 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

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

Ebrahimi, K, Vaidya, U & Elia, N 2019, Robust Optimization via Discrete-Time Saddle Point Algorithm. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9028953, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 2473-2478, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 12/11/19. https://doi.org/10.1109/CDC40024.2019.9028953

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abstract = "We discover discrete-time counterpart of the continuous-time saddle point algorithm developed in [1] for solving robust optimization problems. Under the assumption that the cost function is convex in the decision variable and uncertainties enter concavely in the robust optimization problem, we prove global asymptotic convergence of the saddle-point algorithm to the robust optimal solution. The sub-gradient nature of the proposed discrete-time algorithm allows us to handle robust optimization problems with discontinuous cost function and constraint.",

author = "Keivan Ebrahimi and Umesh Vaidya and Nicola Elia",

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AB - We discover discrete-time counterpart of the continuous-time saddle point algorithm developed in [1] for solving robust optimization problems. Under the assumption that the cost function is convex in the decision variable and uncertainties enter concavely in the robust optimization problem, we prove global asymptotic convergence of the saddle-point algorithm to the robust optimal solution. The sub-gradient nature of the proposed discrete-time algorithm allows us to handle robust optimization problems with discontinuous cost function and constraint.

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Robust Optimization via Discrete-Time Saddle Point Algorithm

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