A situation is considered in which a grenade launcher fires at a target, observes the projectile impact, adjusts the point of aim, fires a second round, adjusts, fires, and so on. A model is developed, based on the assumptions of normal ballistics, perfect observation of impacts, adjustments without error, and a unimodal target destruction function. The problem is to determine optimal adjustments, in order to maximize the probability of target destruction within a given number of rounds. It is shown that seemingly different adjustment procedures are equivalent, if viewed in appropriate coordinate systems. Previous results concerning sequential adjustments which are constrained to be linear functions of observed impact points are extended to the class of translation invariant procedures. Properties of the optimal sequential adjustment procedure, including some related to stochastic approximation, are reviewed. The effects of errors in judging impact positions are discussed. (Author)
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