The approximate subdiierential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdiierentiability might be related to its non-convexity. This motivates to study some topological properties more in detail. As the main result, it is shown that in a Hilbert space setting each weakly compact set may be o...

The concept of compactly epi-Lipschitzian (CEL) sets in locally convex topological spaces was introduced by Borwein and Strojwas [6]. It is an extension of Rockafellar’s concept of epi-Lipschitzian sets [36]. An advantage of the CEL property is that it always holds in finite dimensional spaces and, in contrast to its epi-Lipschitzian predecessor, makes it possible to recapture much of the detai...

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in o...

* Correspondence: [email protected] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract The purpose of this paper is to introduce a new system of general nonlinear regularized nonconvex variational inequalities and verify the equivalence between the proposed system and f...

A Qk(R ) -valued function is essentially a rule assigning k unordered and non necessarily distinct elements of R to each element of its domain set A ⊆ R . For a Qk(R) valued function f we construct a decomposition into k branches that naturally inherit the regularity properties of f . Next we prove that a measurable Qk(R ) -valued function admits a decomposition into k measurable branches. An e...

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend