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Journal of Optimization Theory and Applications

, Volume 92, Issue 2, pp 357–375 | Cite as

Six Kinds of Roughly Convex Functions

  • H. X. Phu
Article

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.

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 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • H. X. Phu
    • 1
  1. 1.Institute of MathematicsNghiado, Tuliem, HanoiVietnam

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