Generalized Invariant Monotonicity and Invexity of Non-differentiable Functions

  • Authors:

  • T. Jabarootian;J. Zafarani

  • Affiliations:

  • Department of Mathematics, University of Isfahan, Isfahan, Iran 81745-163;Department of Mathematics, University of Isfahan, Isfahan, Iran 81745-163

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2006

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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.