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Generalized pseudolinearity

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Abstract

In this paper, we introduce the notion of generalized pseudolinearity for nondifferentiable and nonconvex but locally Lipschitz functions defined on a Banach space. We present some characterizations of generalized pseudolinear functions. The characterizations of the solution set of a nonconvex and nondifferentiable but generalized pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs and η-pseudolinear programs.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  2. Department of Mathematics, University of Isfahan, 81745-163, Isfahan, Iran

    Mahboubeh Rezaei

Authors
  1. Qamrul Hasan Ansari
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  2. Mahboubeh Rezaei
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Correspondence to Qamrul Hasan Ansari.

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Ansari, Q.H., Rezaei, M. Generalized pseudolinearity. Optim Lett 6, 241–251 (2012). https://doi.org/10.1007/s11590-010-0238-2

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  • DOI: https://doi.org/10.1007/s11590-010-0238-2

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