Introduction to sublinear analysis

Basing on the notion of compact subdifferentials, we develop a subdifferential calculus of the first and the second orders beyond the Taylor expansion and extremum theory. We introduce and investigate a comprehensive class of subsmooth maps such that the constructed theory is applicable to them. We develop a technique to investigate one-dimensional extremal variational problems with subsmooth Lagrangians (including sufficient conditions). A number of examples are considered.