Document Type

Technical Report


This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

Number in Series



Applied Mathematics | Mathematics

AMS Subject Classification

49J52, 49J53, 90C29


This research was partly supported by a grant of Technical University Varna, by the USA National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-1292508, and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.