The Space of Star-Shaped Sets and Its Applications in Nonsmooth Optimization

Rubinov AM & Yagubov AA (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: 19 Jul 2016 17:12
URI: http://pure.iiasa.ac.at/2548

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