Conjugate duality in the optimization of the search for a target with generalized conditionally deterministic motion

Abstract

A target moves in Euclideann-spaceR ⁿ according to the generalized conditionally deterministic law. The search density that accumulates on the target during its route determines the probability of detection. A necessary and sufficient condition for the search density α(x, t) to be optimal is first represented, when there are two types of constraints for the search density: pointwise constraints and total-amount constraints. The second part consists of formulation of the dual problem with the aid of sensitivity parameters for the constraints. By using the dual functional, we obtain the maximal error from the minimum value of the primal objective functional for an arbitrary feasible α. Finally, we study the discretized case, which is necessary for numerical calculations.