Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets C for which the distance function dC is continuously differentiable everywhere on an open “tube” of uniform… (More)

The behavior of a minimizing point when an objective function is tilted by adding a small linear term is studied from the perspective of second-order conditions for local optimality. The classical… (More)

Necessary and sufficient conditions are obtained for the Lipschitzian stability of local solutions to finite-dimensional parameterized optimization problems in a very general setting. Properties of… (More)

The question of second-order expansions is taken up for a class of functions of importance in optimization, namely Moreau envelope regularizations of nonsmooth functions f . It is shown that when f… (More)

Attouch's Theorem, which gives on a reflexive Banach space the equivalence between the Mosco epi-convergence of a sequence of convex functions and the graph convergence of the associated sequence of… (More)

Subgradient mappings associated with various convex and nonconvex functions are a vehicle for stating optimality conditions, and their proto-differentiability plays a role therefore in the… (More)

18. A. D. Iooe, \Variational analysis of a composite function: a formula for the lower second order epi-derivative," J. 843{865. 21. R. A. Poliquin, \An extension of Attouch's Theorem and its… (More)

In 1977, Hedy Attouch established that a sequence of (closed proper) convex functions epi-converges to a convex function if and only if the graphs of the subdifferentials converge (in the Mosco… (More)

Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality… (More)