On maximization of the integral of a bell‐shaped function over a symmetric set

Dennis C. Gilliland

Naval Research Logistics Quarterly, 1968, vol. 15, issue 4, 507-516

Abstract: Given a target T in Euclidean n‐space Rn and a point bomb whose point of impact in Rn is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit va(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for va(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.

Date: 1968
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https://doi.org/10.1002/nav.3800150404

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:15:y:1968:i:4:p:507-516

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