VARIANTS OF THE KUHN TUCKER SUFFICIENT CONDITIONS IN CONES OF NONNEGATIVE FUNCTIONS

Second-order sufficient conditions of the Kuhn-Tucker type are proved for certain constrained minimization problems on sets of nonnegative L(p) functions, with p is-an-element-of [2, infinity]. The objective functions for these problems have specially structured bilinear second Gateaux differentials that are bounded with respect to the L2 norm and vary continuously with respect to the L2 norm on L(p). Structure and smoothness conditions of this sort are satisfied by nontrivial classes of constrained-input Bolza optimal control problems, and in this context, the associated Kuhn-Tucker sufficient conditions yield a partial extension of the classical weak sufficiency theory in the calculus of variations.