Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

This paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main focus is the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order...

We derive a simple formula for the second-order subdifferential of the maximum of coordinates which allows us to construct this set immediately from its argument and the direction to which it is applied. This formula can be combined with a chain rule recently proved by Mordukhovich and Rockafellar [9] in order to derive a similarly simple formula for the extended partial second-order subdiffere...

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes nonsmooth optimization problems. These are based on theory calculations second-order subdifferentials functions with employing machinery variational analysis differentiation. First we develop a superlinearly Newton-type algorithm class continuously differentiabl...

We introduce and study a new class of subdifferentials associated with arbitrary functions. Among the questions considered are: connection with other derivative-like objects (e.g. derivatives, convex subdifferentials, generalized gradients of Clarke and derívate containers of Warga), calculus of approximate subdifferentials and applications to analysis of set-valued maps and to optimization. It...

In this paper, we present new partial subdifferentiation formulas in nonsmooth analysis, based upon the study of two directional derivatives. Simple applications of these formulas include a new elementary proof of Rademacher’s Theorem in Rn, as well as some results on Gâteaux and Fréchet differentiability for locally Lipschitz functions in a separable Hilbert space. Résumé. Dans cet article, no...