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On existence of efficient solutions to vector optimization problems in Banach spaces


Abstract


In this paper, we present a new characterization of lower semicontinuity of vectorvalued mappings and apply it to the solvability of vector optimization problems in Banach spaces. With this aim we introduce a class of vector-valued mappings that is more wider than the class of vector-valued mappings with the "typical" properties of lower semi-continuity including quasi and order lower semi-continuity. We show that in this case the corresponding vector optimization problems have non-empty sets of efficient solutions.

DOI Code: 10.1285/i15900932v30n1p25

Keywords:
lower semicontinuity; vector-valued optimization; efficient solutions; partially ordered spaces

Classification: 46B40; 49J45; 90C29; 49N90

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