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Conditions for Exact Convex Relaxation and No Spurious Local Optima

Zhou, Fengyu and Low, Steven H. (2021) Conditions for Exact Convex Relaxation and No Spurious Local Optima. IEEE Transactions on Control of Network Systems . ISSN 2325-5870. doi:10.1109/TCNS.2021.3112758. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20210510-075841014

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Abstract

Non-convex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that relaxation is usually exact and local algorithms usually converge to a global optimum. In this paper, we study conditions which are sufficient or necessary for such non-convex problems to simultaneously have exact relaxation and no spurious local optima. Those conditions help us explain the widespread empirical experience that local algorithms for OPF problems often work extremely well.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TCNS.2021.3112758DOIArticle
https://arxiv.org/abs/2102.11946arXivDiscussion Paper
ORCID:
AuthorORCID
Zhou, Fengyu0000-0002-2639-6491
Low, Steven H.0000-0001-6476-3048
Additional Information:© 2021 IEEE.
Subject Keywords:Convex relaxation, local optimum, optimal power flow, semidefinite program
DOI:10.1109/TCNS.2021.3112758
Record Number:CaltechAUTHORS:20210510-075841014
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210510-075841014
Official Citation:F. Zhou and S. Low, "Conditions for Exact Convex Relaxation and No Spurious Local Optima," in IEEE Transactions on Control of Network Systems, doi: 10.1109/TCNS.2021.3112758
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109018
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 May 2021 19:56
Last Modified:14 Dec 2021 21:39

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