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Journal of Global Optimization

, Volume 36, Issue 4, pp 537–564 | Cite as

Generalized Invariant Monotonicity and Invexity of Non-differentiable Functions

  • T. Jabarootian
  • J. Zafarani
Article

Abstract

This paper is devoted to the study of relationships between several kinds of generalized invexity of locally Lipschitz functions and generalized monotonicity of corresponding Clarke’s subdifferentials. In particular, some necessary and sufficient conditions of being a locally Lipschitz function invex, quasiinvex or pseudoinvex are given in terms of momotonicity, quasimonotonicity and pseudomonotonicity of its Clarke’s subdifferential, respectively. As an application of our results, the existence of the solutions of the variational-like inequality problems as well as the mathematical programming problems (MP) is given. Our results extend and unify the well known earlier works of many authors.

Keywords

generalized invariant monotone generalized invex functions Clarke’s subdifferential variational-like problem mathematical programming problem 

Mathematics Subject Classifications

26B25 49J52 90C30 49J40 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

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