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Six Kinds of Roughly Convex Functions

Author

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  • H. X. Phu

    (Institute of Mathematics)

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.

Suggested Citation

  • H. X. Phu, 1997. "Six Kinds of Roughly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 357-375, February.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:2:d:10.1023_a:1022611314673
    DOI: 10.1023/A:1022611314673
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    Cited by:

    1. H.X. Phu & N.N. Hai & P.T. An, 2003. "Piecewise Constant Roughly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 415-438, May.
    2. Hoang Phu, 2008. "Supremizers of inner γ-convex functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 207-222, April.
    3. H.X. Phu, 2003. "Strictly and Roughly Convexlike Functions," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 139-156, April.

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