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| Paper IPM / M / 16896 |
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| Abstract: | |
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This paper deals with approximate weak minimal solutions of setvalued optimization problems under vector and set optimality criteria. The
relationships between various concepts of approximate weak minimal solutions
are investigated. Some topological properties and existence theorems of these
solutions are given. It is shown that for set-valued optimization problems with
upper (outer) cone-semicontinuous objective values or closed objective maps
the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed. By using the polar cone and two scalarization
processes, some necessary and sufficient optimality conditions in the sense of
vector and set criteria are provided.
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