Generalized pseudolinearity

Generalized pseudolinearity

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Article ID: iaor2012651
Volume: 6
Issue: 2
Start Page Number: 241
End Page Number: 251
Publication Date: Feb 2012
Journal: Optimization Letters
Authors: ,
Keywords: linearization, Banach space, Lipschitz functions
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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