Generalized gradients of Lipschitz functionals

AbstractThe purpose of this article is threefold: (i) to present in a unified fashion the theory of generalized gradients, whose elements are at present scattered in various sources; (ii) to give an account of the ways in which the theory has been applied; (iii) to prove new results concerning generalized gradients of summation functionals, pointwise maxima, and integral functionals on subspaces of L∞. These last-mentioned formulas are obtained with an eye to future applications in the calculus of variations and optimal control. Their proofs can be regarded as applications of the existing theory of subgradients of convex functionals as developed by Rockafellar, Ioffe and Levin, Valadier, and others