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Strictly and Roughly Convexlike Functions

Author

Listed:
  • H.X. Phu

    (Institute of Mathematics)

Abstract

A function $$f:D \subseteq \mathbb{R}^n \to \mathbb{R}$$ is said to be strictly and roughly convexlike with respect to the roughness degree r > 0 (for short, strictly r-convexlike) provided that, for all x 0, x 1 ∈ D satisfying ||x 0 − x 1|| > r, there exists a λ ∈ ]0, 1[ such that $$f((1 - \lambda )x_0 + \lambda x_1 )

Suggested Citation

  • H.X. Phu, 2003. "Strictly and Roughly Convexlike Functions," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 139-156, April.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:1:d:10.1023_a:1023608624625
    DOI: 10.1023/A:1023608624625
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    References listed on IDEAS

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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    2. H. X. Phu, 1997. "Six Kinds of Roughly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 357-375, February.
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    Cited by:

    1. Hoang Phu & Vo Pho, 2010. "Global infimum of strictly convex quadratic functions with bounded perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 327-345, October.

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