Emrah KARAMAN, İlknur ATASEVER GÜVENÇ, Mustafa SOYERTEM, Didem TOZKAN, Mahide KÜÇÜK, Yalçın KÜÇÜK

201207

A vectorization for nonconvex set-valued optimization

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.
Keywords:

Set-valued optimization, nonconvex optimization, vectorization, optimality conditions,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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