Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

Vsevolod Ivanov ()

Journal of Global Optimization, 2013, vol. 57, issue 3, 677-693

Abstract: In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to Mangasarian (Oper Res Lett 7:21–26, 1988 ). A positive function p appears in the most results. It is replaced by the number 1 if the function is convex and its domain of definition is convex, too. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Pseudoconvex functions; Semistrictly quasiconvex functions; Nonsmooth analysis; Characterizations of the solution set of a set constrained optimization problem; Optimality conditions; 26B25; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10898-012-9956-6

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