Six Kinds of Roughly Convex Functions

H. X. Phu
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H. X. Phu: Institute of Mathematics

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 2, No 8, 357-375

Abstract: Abstract This paper considers six kinds of roughly convex functions, namely: δ-convex, midpoint δ-convex, ρ-convex, γ-convex, lightly γ-convex, and midpoint γ-convex functions. The relations between these concepts are presented. It is pointed out that these roughly convex functions have two optimization properties: each r-local minimizer is a global minimizer, and if they assume their maximum on a bounded convex domain D (in a Hilbert space), then they do so at least at one r-extreme point of D, where r denotes the roughness degree of these functions. Furthermore, analytical properties are investigated, such as boundedness, continuity, and conservation properties.

Keywords: Generalized convexity; roughly convex functions; δ-convex functions; midpoint δ-convex functions; ρ-convex functions; γ-convex functions; lightly γ-convex functions; midpoint γ-convex functions; boundedness; continuity; differentiability (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1022611314673

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