Technical Note—Conditions for Global Optimality in Nonlinear Programming

This note presents necessary and sufficient conditions for a point x* to be a global solution of the problem of maximizing f subject to x ∈ S. The conditions are equivalent to the divergence or convergence of an infinite sequence, each of whose terms involves the integral of a power of f taken over S. A useful corollary is derived that characterizes the sequence as one that is eventually monotone increasing if and only if x* is not a global solution. A small example illustrates these results.