# Selection of nonextremal candidates from a random sequence

@article{Rose1982SelectionON, title={Selection of nonextremal candidates from a random sequence}, author={John S. Rose}, journal={Journal of Optimization Theory and Applications}, year={1982}, volume={38}, pages={207-219} }

Problems of optimal choice generally invoke monotone preference functions; consequently, optimal strategies consider stopping the sequence only when extremal (best/worst) or nearly extremal candidates are presented. The objective of the present investigation is to select a candidate representative of the entire sequence. In particular, selection of the median object and selection of any object from a set of middle ranks are considered.

## 7 Citations

A rank-based selection with cardinal payoffs and a cost of choice

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A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$,…

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In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of n candidates when their relative ranks are observed sequentially. This problem…

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The focus is on problems that require a decision-maker to choose a candidate from a pool of sequential applicants with no recall, in the vein of previously studied Cayley-Moser, Secretary and Sultan's Dowry problems.

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We present a new variant of the secretary problem: Let An be a totally ordered set of n applicants. Given P ⊆ An and x ∈ An, let rr(P, x) = |{z ∈ P | z ≤ x}| be the relative rank of x with regard to…

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We present a new variant of the secretary problem. Let An be a totally ordered set of n applicants. Given P ⊆ An and x ∈ An, let rr(P, x) = |{z ∈ P | z ≤ x}| be the relative rank of x with regard to…

Directional derivative of the marginal function in nonlinear programming

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Under the constant rank regularity assumption, a maximin formula is obtained for the directional derivative of the marginal value function of a perturbed nonlinear mathematical programming problem.

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