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Signomial and polynomial optimization via relative entropy and partial dualization

Murray, Riley and Chandrasekaran, Venkat and Wierman, Adam (2020) Signomial and polynomial optimization via relative entropy and partial dualization. Mathematical Programming Computation . ISSN 1867-2949. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20201014-133741550

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Abstract

We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way which enables partial dualization of certain structured constraints. This more general approach retains key properties of ordinary SAGE relaxations (e.g. sparsity preservation), and inspires a projective method of solution recovery which respects partial dualization. We illustrate the utility of our methodology with a range of examples from the global optimization literature, along with a publicly available software package.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s12532-020-00193-4DOIArticle
https://arxiv.org/abs/1907.00814arXivDiscussion Paper
https://rileyjmurray.github.io/sageoptRelated ItemSoftware
Additional Information:© 2020 Springer-Verlag. Received 21 July 2019; Accepted 11 August 2020; Published 14 October 2020. The authors thank Fangzhou Xiao and two anonymous referees for helpful feedback. R.M. was supported in part by an NSF Graduate Research Fellowship, NSF grants CCF-1350590 and CCF-1637598, and AFOSR grant FA9550-16-1-0210. V.C. was supported in part by NSF grants CCF-1350590 and CCF-1637598, AFOSR grant FA9550-16-1-0210, and a Sloan Research Fellowship. A.W. was supported in part by NSF grant CCF-1637598.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
NSFCCF-1350590
NSFCCF-1637598
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0210
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Global optimization; Exponential cone programs; SAGE certificates; SOS certificates; Signomial programming
Record Number:CaltechAUTHORS:20201014-133741550
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201014-133741550
Official Citation:Murray, R., Chandrasekaran, V. & Wierman, A. Signomial and polynomial optimization via relative entropy and partial dualization. Math. Prog. Comp. (2020). https://doi.org/10.1007/s12532-020-00193-4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106063
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Oct 2020 21:05
Last Modified:14 Oct 2020 21:25

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