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Paper   IPM / M / 16896
School of Mathematics
  Title:   Approximate weak minimal solutions of set-valued optimization problems
  Author(s):  Soqra Khoshkhabar-amiranloo
  Status:   To Appear
  Journal: J. Operations Research Soc.China
  Supported by:  IPM
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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