Abstract
The study of quasidifferentiable functions is based on the properties of the space of convex sets. One very important concept in convex analysis is that of the gauge of a set. However, the definition of a gauge does not require convexity, and therefore the notion of a gauge can be extended beyond convex sets to a much wider class of sets. In this paper the authors develop a theory of gauge functions and study some properties of star-shaped sets. The results are then used to study nonsmooth extremal problems (of which problems involving quasidifferentiable functions represent a special class).
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© 1986 The Mathematical Programming Society, Inc.
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Rubinov, A.M., Yagubov, A.A. (1986). The space of star-shaped sets and its applications in nonsmooth optimization. In: Demyanov, V.F., Dixon, L.C.W. (eds) Quasidifferential Calculus. Mathematical Programming Studies, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121146
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DOI: https://doi.org/10.1007/BFb0121146
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