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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. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210510-075841014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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2102.11946arXivDiscussion Paper
ORCID:
AuthorORCID
Zhou, Fengyu0000-0002-2639-6491
Low, Steven H.0000-0001-6476-3048
Subject Keywords:Convex relaxation, local optimum, optimal power flow, semidefinite program
Record Number:CaltechAUTHORS:20210510-075841014
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210510-075841014
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:10 May 2021 19:56

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