Abstract
A.generalized approximation of the subdifferential called the (ε,µ)-subdifferential is introduced for upper-semicontinuously directionally differentiable functions. The most attractive and important property of the (ε,µ)-subdifferential is that it can be taken to be a continuous mapping; this, in its turn, allows us to construct numerical methods for finding stationary points.
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References
Yu.G. Borisovich, B.G. Gelman, A.D. Myshkis and V.V. Obihovski. Multivalued mappings (in Russian). Achievements of Science and Engineering: Mathematical Analysis, 19 (1982) 127 - 230.
V.F. Demyanov and V.K. Shomesova. Conditional subdifferentials of convex functions. Soviet Math. Dokl., 19(5) (1978)1181-1185.
V.F. Demyanov and L.V. Vasiliev. Nondifferentiable Optimization. Nauka, Moscow, 1981.
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© 1985 Springer-Verlag Berlin Heidelberg
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Rubinov, A.M. (1985). Upper-Semicontinuously Directionally Differentiable Functions. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_7
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DOI: https://doi.org/10.1007/978-3-662-12603-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15979-7
Online ISBN: 978-3-662-12603-5
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