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Rubinov, A.M. & Yagubov, A.A. (1984). The Space of Star-Shaped Sets and Its Applications in Nonsmooth Optimization. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-029
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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).
| Item Type: | Monograph (IIASA Collaborative Paper) |
|---|---|
| Uncontrolled Keywords: | gauge; star-shaped sets; positively homogeneous functions; directional derivatives; nonsmooth optimization; quasidifferentiable functions; necessary conditions |
| Research Programs: | System and Decision Sciences - Core (SDS) |
| Depositing User: | IIASA Import |
| Date Deposited: | 15 Jan 2016 01:55 |
| Last Modified: | 27 Aug 2021 17:12 |
| URI: | https://pure.iiasa.ac.at/2548 |
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