Invariant Pseudolinearity with Applications

Qamrul Hasan Ansari () and Mahboubeh Rezaei ()
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Qamrul Hasan Ansari: Aligarh Muslim University
Mahboubeh Rezaei: University of Isfahan

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 3, No 3, 587-601

Abstract: Abstract In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, 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.

Keywords: Invex sets; Pseudoinvexity; Invariant pseudolinearity; Dini directional derivatives; Nonsmooth variational-like inequalities; Solution sets of a program (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9979-z

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