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A Sufficient Condition for Local Optima to be Globally Optimal

Zhou, Fengyu and Low, Steven H. (2020) A Sufficient Condition for Local Optima to be Globally Optimal. In: 2020 59th IEEE Conference on Decision and Control (CDC). IEEE , pp. 1684-1690. ISBN 9781728174471. https://resolver.caltech.edu/CaltechAUTHORS:20210121-152558409

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Abstract

Consider an optimization problem with a convex cost function but a non-convex compact feasible set X, and its relaxation with a compact and convex feasible set X̂ ⊃ X. We prove that if from any point x ∈ X̂∖X there is a path connecting x to X along which both the cost function and a Lyapunov-like function are improvable, then any local optimum in X for the original non-convex problem is a global optimum. We use this result to show that, for AC optimal power flow problems, a wellknown sufficient condition for exact relaxation also guarantees that all its local optima are globally optimal. This helps explain the widespread empirical experience that local algorithms for optimal power flow problems often work extremely well.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/cdc42340.2020.9303868DOIArticle
ORCID:
AuthorORCID
Zhou, Fengyu0000-0002-2639-6491
Low, Steven H.0000-0001-6476-3048
Additional Information:© 2020 IEEE. This work was funded by NSF through grants CCF 1637598, ECCS 1619352, ECCS 1931662 and CPS ECCS 1739355.
Funders:
Funding AgencyGrant Number
NSFCCF-1637598
NSFECCS-1619352
NSFECCS-1931662
NSFECCS-1739355
Record Number:CaltechAUTHORS:20210121-152558409
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210121-152558409
Official Citation:F. Zhou and S. H. Low, "A Sufficient Condition for Local Optima to be Globally Optimal," 2020 59th IEEE Conference on Decision and Control (CDC), Jeju Island, Korea (South), 2020, pp. 1684-1690, doi: 10.1109/CDC42340.2020.9303868
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107644
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Jan 2021 23:53
Last Modified:22 Jan 2021 00:11

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