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Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives
Journal article   Open access  Peer reviewed

Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives

El-Desouky Rahmo and Marcin Studniarski
Journal of mathematical analysis and applications, Vol.393(1), pp.212-221
01/09/2012
DOI: https://doi.org/10.1016/j.jmaa.2012.04.021

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We introduce lower and upper limits of vector-valued functions with respect to the usual positive cone in a finite-dimensional space. Using these concepts, we extend the definitions of m-th order lower and upper directional derivatives introduced in Studniarski (1986) [1] to vector-valued functions, and prove some necessary and sufficient conditions for strict local Pareto minimizers of order m. (C) 2012 Elsevier Inc. All rights reserved.
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https://doi.org/10.1016/j.jmaa.2012.04.021View
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