A vectorization for nonconvex set-valued optimization

Authors : Emrah KARAMAN, İlknur Atasever GÜVENÇ, Mustafa SOYERTEM, Didem TOZKAN, Mahide KÜÇÜK, Yalçin KÜÇÜK

Pages : 1815-1832

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :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