This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefinite...

Developing first order optimality conditions for two-stage stochastic mathematical programs with equilibrium constraints (SMPECs) whose second stage problem has multiple equilibria/solutions is a challenging undone work. In this paper we take this challenge by considering a general class of two-stage SMPECs whose equilibrium constraints are represented by a parametric variational inequality (wh...

In general Banach space setting, we study the perturbed distance function d J S (·) determined by a closed subset S and a lower semicontinuous function J (·). In particular, we show that the Fréchet subdifferential and the proximal subdifferential of a perturbed distance function are representable by virtue of corresponding normal cones of S and subdifferentials of J (·).

In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions f...

We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are ob...

We establish representations of a monotone mapping as the sum of a maximal subdifferential mapping and a ‘remainder’ monotone mapping, where the remainder is either skew linear, or more broadly ‘acyclic’, in the sense that it contains no nontrivial subdifferential component. Examples are given of indecomposable and acyclic operators. In particular, we present an explicit nonlinear acyclic opera...

The aim of this note is to give an alternative proof for a recent result due to Dorsch, Jongen and Shikhman, which provides an upper estimate for the Clarke subdifferential of an infimal value function. We show the validity of this result under a weaker condition than the one assumed in the mentioned paper, while the use of the Mordukhovich subdifferential, as an intermediate step, will conside...