Document Type

Technical Report


The 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 attention is paid to 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 sub differential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and their major specifications are applied then to the study of tilt stability of local minimizers for important classes of problems in constrained optimization that include, in particular, problems of nonlinear programming and certain classes of extended nonlinear programs described in composite terms.

Number in Series



Applied Mathematics | Mathematics

AMS Subject Classification

49J52, 90C30, 90C31


This research was partly supported by the National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-12092508, and by the Portuguese Foundation of Science and Technologies under grant MAT /11109.