Volume 57, Issue 4
Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem

Giangvuthanh Nguyen, Xiang Xu & Yanxiang Zhao

J. Math. Study, 57 (2024), pp. 476-485.

Published online: 2024-12

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  • 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.

  • AMS Subject Headings

26A06, 49K05

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COPYRIGHT: © Global Science Press

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@Article{JMS-57-476, author = {Nguyen , GiangvuthanhXu , Xiang and Zhao , Yanxiang}, title = {Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {57}, number = {4}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n4.24.05}, url = {http://global-sci.org/intro/article_detail/jms/23713.html} }
TY - JOUR T1 - Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem AU - Nguyen , Giangvuthanh AU - Xu , Xiang AU - Zhao , Yanxiang JO - Journal of Mathematical Study VL - 4 SP - 476 EP - 485 PY - 2024 DA - 2024/12 SN - 57 DO - http://doi.org/10.4208/jms.v57n4.24.05 UR - https://global-sci.org/intro/article_detail/jms/23713.html KW - Secretary problem, adaptive algorithm, expected score, uniqueness of maximum points. AB -

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.

Nguyen , GiangvuthanhXu , Xiang and Zhao , Yanxiang. (2024). Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem. Journal of Mathematical Study. 57 (4). 476-485. doi:10.4208/jms.v57n4.24.05
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