×

Generalized derivatives for non-smooth functions. (English) Zbl 0778.49022

This paper formulates an extension of the classical differential calculus to a large class of nonsmooth functions of finitely many variables which often arise in nonsmooth optimization. The authors provide a framework for studying the generalized derivatives and the higher order directional derivatives and prove some analogies to the well-known theorems of the classical calculus in the generalized setting. A few interesting results are presented for the quasi-differentiable functions or the approximate quasi-differentiable functions.

MSC:

49J52 Nonsmooth analysis
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
90C30 Nonlinear programming
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
PDFBibTeX XMLCite