Subdifferentials of Nonconvex Supremum Functions and Their Applications to Semi-infinite and Infinite Programs with Lipschitzian Data

The paper is devoted to the subdifferential study and applications of the supremum of uniformly Lipschitzian functions over arbitrary index sets with no topology. Based on advanced techniques of variational analysis, we evaluate major subdifferentials of the supremum functions in the general framework of Asplund (in particular, reflexive) spaces with no convexity or relaxation assumptions. The results obtained are applied to deriving new necessary optimality conditions for nonsmooth and nonconvex problems of semi-infinite and infinite programming.