Abstract
In this paper we present a concept of the construction of generalized gradients by considering a development of directional derivatives into spherical harmonics. This leads to a derivation system as a system of generalized partial derivatives. Necessary conditions for local extrema for a broad class of not necessarily differentiable function can be given and a characterization of points of differentiability can be proved by using generalized gradients.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Clarke FH (1989) Optimization and Nonsmooth Analysis. Wiley
Demjanov VF, Rubinov AM (1986) Quasidifferentiable Calculus. Optimization Software Inc
Heymann WK, Kennedy PB (1976) Subharmonic Functions, Vol I. Academic Press
Müller K (1966) Spherical Polynomials. Lecture Notes in Mathematics, Vol 17. Springer
Pallaschke D, Recht P, Urbanski R (1987) On Extensions of the Second-Order Derivative. Bull Acad Polon, Sci Ser Func Anal, pp 751–763
Zygmund A (1988) Trigonometric Series, Vol I, II. Cambridge Univ Press
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Recht, P. On generalized gradients. ZOR - Methods and Models of Operations Research 36, 201–210 (1992). https://doi.org/10.1007/BF01415887
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01415887