A Note on Ordinal Submodularity
Satoru Fujishige, Ryuhei Mizutani
TL;DR
This paper explores various classes of ordinally submodular functions on finite Boolean lattices, providing characterizations of their minimizers to advance understanding of their structure and optimization.
Contribution
It introduces characterizations of minimizers for several classes of ordinally submodular functions, expanding theoretical understanding in this area.
Findings
Characterizations of minimizers for different classes of ordinally submodular functions
Insights into the structure of ordinally submodular functions on Boolean lattices
Theoretical foundations for optimization of ordinally submodular functions
Abstract
Notions of ordinal submodularity/supermodularity have been introduced and studied in the literature. We consider several classes of ordinally submodular functions defined on finite Boolean lattices and give characterizations of the set of minimizers of ordinally submodular functions.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topology and Set Theory · Advanced Banach Space Theory