Constrained Optimization of Functionals with Search Theory Applications

We find necessary and sufficient conditions for maximizing a wide class of nonlinear, nonseparable functionals under separable constraints. The crucial restriction on the functionals is that they have a Gateaux differential which is a linear functional with a kernel. The conditions obtained can be applied to a large variety of optimal search problems involving moving targets when effort is infinitely divisible in space. Moreover, the conditions have been used to construct very efficient algorithms for solving these problems. It is conjectured that these results are useful in a general class of optimization problems that extend well beyond the search theory examples presented in this paper.