Signomial and polynomial optimization via relative entropy and partial dualization

  • 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.

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Metadaten
Author:Riley Murray, Venkat Chandrasekaran, Adam Wierman
DOI:https://doi.org/10.1007/s12532-020-00193-4
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2020
Tag:Software; Theoretical Computer Science
Volume:13
Issue:2
Page Number:39
First Page:257
Last Page:295
Mathematical Programming Computation :MPC 2021 - Issue 2
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