Abstract
The aim of this paper is to study optimality conditions for strict local minima to constrained mathematical problems governed by scalar and vectorial mappings. Unlike other papers in literature dealing with strict efficiency, we work here with mappings defined on infinite dimensional normed vector spaces. Firstly, we (mainly) consider the case of nonsmooth scalar mappings and we use the Fréchet and Mordukhovich subdifferentials in order to provide optimality conditions. Secondly, we present some methods to reduce the study of strict vectorial minima to the case of strict scalar minima by means of some scalarization techniques. In this vectorial framework we treat separately the case where the ordering cone has non-empty interior and the case where it has empty interior.
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This research was supported by the CNCSIS Grant Code ID_379/2007.
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Durea, M. Remarks on strict efficiency in scalar and vector optimization. J Glob Optim 47, 13–27 (2010). https://doi.org/10.1007/s10898-009-9453-8
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DOI: https://doi.org/10.1007/s10898-009-9453-8