Quasidifferentiability of real-valued functions and local extremum conditions
For real-valued functions defined on a finite-dimensional Euclidean space, we introduce the concepts of \(\epsilon\)-quasidifferentials (lower and upper) and quasidifferentiability (lower, upper). The class of functions having the property of quasidifferentiability in the sense of the present paper is sufficiently broad. We note that any locally Lipschitz function is lower and upper quasidifferentiable. The fundamental formulas of the calculus of \(\epsilon\)-quasidifferentials are given. For functions having lower (upper) \(\epsilon\)-quasidifferential, we establish both necessary and also sufficient conditions for a local minimum (maximum). We show that for a wide class of functions, necessary and also sufficient conditions for a local minimum (maximum) can be formulated in terms of quasidifferentiable lower (upper) local approximations.
scientific article; zbMATH DE number 3909180
scientific article