Uniqueness of Maximum Points of a Sequence of Functions Arising from an Adapted Algorithm for ‘the Secretary Problem’

Authors

Boning Wang, Old Dominion UniversityFollow
Giang Vu Thanh Nguyen, Old Dominion UniversityFollow

Disciplines

Other Mathematics

Document Type

Article

DOI

https://doi.org/10.25778/kyww-br79

Abstract

This paper is aimed at a sequence of functions that is extended from an adaptive algorithm of the classical ‘secretary problem’. It was proved in Nguyen et al. (2024) the uniqueness of maximizers of a function sequence that represents the expected score of an element in a ‘candidate’ sequence. This function sequence is indeed considered as a special case of an extended function sequence that corresponds to the case α = 0. More specifically, we are motivated to prove the uniqueness of maximizers for this extended function sequence in the case α = 1. Nevertheless, the corresponding proof is rather challenging and completely different from the former case α = 0 discussed in Nguyen et al. (2024)

Recommended Citation

Wang, Boning and Nguyen, Giang Vu Thanh (2024) "Uniqueness of Maximum Points of a Sequence of Functions Arising from an Adapted Algorithm for ‘the Secretary Problem’," OUR Journal: ODU Undergraduate Research Journal: Vol. 11, Article 4.
DOI: https://doi.org/10.25778/kyww-br79
Available at: https://digitalcommons.odu.edu/ourj/vol11/iss1/4