Scalarization method for Levitin–Polyak well‐posedness of vectorial optimization problems

Scalarization method for Levitin–Polyak well‐posedness of vectorial optimization problems

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Article ID: iaor2013283
Volume: 76
Issue: 3
Start Page Number: 361
End Page Number: 375
Publication Date: Dec 2012
Journal: Mathematical Methods of Operations Research
Authors: ,
Keywords: vector optimization
Abstract:

In this paper, we develop a method of study of Levitin–Polyak well‐posedness notions for vector valued optimization problems using a class of scalar optimization problems. We first introduce a non‐linear scalarization function and consider its corresponding properties. We also introduce the Furi–Vignoli type measure and Dontchev–Zolezzi type measure to scalar optimization problems and vectorial optimization problems, respectively. Finally, we construct the equivalence relations between the Levitin–Polyak well‐posedness of scalar optimization problems and the vectorial optimization problems.

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