The optimal distribution of search effort: existence, uniqueness and the minimax solution

The detection search problem, one of distributing limited resources so as to maximize the detection probability in the single-try search for a concealed target with known probability density, is analyzed. Under fairly general assumptions, the optimal search density uniquely exists when the detection index is governed by the law of diminishing returns and another simple regularity condition. Numerical procedure based on the bisection method, which is guaranteed to converge if the solution uniquely exists, may be used to solve for the optimal search density and the associated Lagrange multiplier. When it is not possible to confidently estimate the target a priori probability density, the minimax solution guarantees a positive detection probability at the expense of degradation in performance