Title	Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures
Creator	Long, Daniel Zhuoyu
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-01-17T16:55
Description	This work presents a systematic study of the preservation of supermodularity under parametric optimization, that allows us to derive complementarity among parameters and monotone structural properties of optimal policies in many operations models. We introduce new concepts of mostly-lattice and additive mostly-lattice, which significantly generalize the commonly imposed lattice condition, and use them to establish the necessary and sufficient conditions on the feasible set so that supermodularity can be preserved under various assumptions on the objective functions. We further identify some classes of polyhedral sets which satisfy these concepts. Finally, we illustrate how our results can be used on a two-stage optimization problem.
Extent	37.0
Subject	Mathematics; Operations research, mathematical programming; Computer science; Applied computer science
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Chinese University of Hong Kong
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-07-17
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0379890
URI	http://hdl.handle.net/2429/71027
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures Long, Daniel Zhuoyu

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