Year: 2024
Author: Giangvuthanh Nguyen, Xiang Xu, Yanxiang Zhao
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 476–485
Abstract
In this paper, we study some basic analytic properties of a sequence of functions $\{S^{\mu,σ}_n\}$ that is directly derived in an adaptive algorithm originating from the classical score-based secretary problem. More specifically, we show that: 1. the uniqueness of maximum points of the function sequence $\{S^{\mu,σ}_n\};$ 2. the maximum point sequence of $\{S^{\mu,σ}_n\}$ monotone increases to infinity as $n$ tends to infinity. All of the proofs are elementary but nontrivial.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n4.24.05
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 476–485
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Secretary problem adaptive algorithm expected score uniqueness of maximum points.