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 - <p style="text-align: justify;">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.</p>