Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

Fernando García-Castaño (), Miguel Ángel Melguizo-Padial () and G. Parzanese ()
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Fernando García-Castaño: University of Alicante
Miguel Ángel Melguizo-Padial: University of Alicante
G. Parzanese: University of Alicante

Mathematical Methods of Operations Research, 2023, vol. 97, issue 3, No 4, 367-382

Abstract: Abstract We show that under a separation property, a $${{{\mathcal {Q}}}}$$ Q -minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.

Keywords: Scalarization; Proper efficiency; $${{{\mathcal {Q}}}}$$ Q -minimal point; Approximate proper efficiency; Nonconvex vector optimization; Nonlinear cone separation; 90C26; 90C29; 90C30; 90C46; 49K27; 46N10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00818-z

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