In this paper, we present a new characterization of lower semicontinuity of vector-valued 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.
On existence of efficient solutions to vector optimization problems in Banach spaces
MANZO, Rosanna;
2010-01-01
Abstract
In this paper, we present a new characterization of lower semicontinuity of vector-valued 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.File in questo prodotto:
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