A simple proof for the convexity of the Choquet integral
Aur\'elien Alfonsi
TL;DR
This paper provides an elementary and direct proof demonstrating that the Choquet integral is convex when the underlying set function is submodular, simplifying understanding of its mathematical properties.
Contribution
It introduces a straightforward proof of the convexity of the Choquet integral under submodularity, enhancing theoretical clarity.
Findings
Convexity of the Choquet integral proven for submodular set functions
Elementary proof simplifies previous complex demonstrations
Reinforces the mathematical foundation of the Choquet integral
Abstract
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
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Taxonomy
TopicsMulti-Criteria Decision Making · Mathematical Inequalities and Applications · Optimization and Variational Analysis