Pallaschke, D.; Recht, P.; Urbański, R. Generalized derivatives for non-smooth functions. (English) Zbl 0778.49022 Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 31, 97-114 (1991). 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. Reviewer: Wang Shouyang (Beijing) 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 Keywords:nondifferentiability; Fourier analysis; nonsmooth functions of finitely many variables; nonsmooth optimization; generalized derivatives; quasi- differentiable functions PDFBibTeX XMLCite \textit{D. Pallaschke} et al., Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 31, 97--114 (1991; Zbl 0778.49022)