Abstract
A class of Lipschitz quasidifferentiable functions is described for which the exact representation of the Clarke subdifferential in terms of a quasidifferential holds. The sufficient conditions formulated are different from those previously established by Rubinov and Akhundov.
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Clarke, F. H.,Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, New York, 1983.
Demyanov, V. F., andRubinov, A. M.,Foundations of Nonsmooth Analysis and Quasidifferential Calculus, Nauka, Moscow, Russia, 1990 (in Russian).
Demyanov, V. F.,On a Relation between the Clarke Subdifferential and the Quasidifferential, Vestnik Leningrad University, Mathematics, Vol. 13, pp. 183–189, 1981.
Rubinov, A. M., andAkhundov, I. S.,The Difference of Compact Sets in the Sense of Demyanov and Its Application to Nonsmooth Analysis, Optimization, Vol. 23, pp. 179–188, 1992.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Peretti, A., andSutti, C.,Monotone, Convex, and First-Order Maps in the Optimization of Nonsmooth Lipschitz Functions, Optimization, Vol. 33, pp. 105–117, 1995.
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Communicated by F. Giannessi
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Demyanov, V.F., Sutti, C. Representation of the Clarke subdifferential for a regular quasidifferentiable function. J Optim Theory Appl 87, 553–561 (1995). https://doi.org/10.1007/BF02192133
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DOI: https://doi.org/10.1007/BF02192133