A unified minimal solution in set optimization

Khushboo () and C. S. Lalitha ()
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Khushboo: University of Delhi
C. S. Lalitha: University of Delhi South Campus

Journal of Global Optimization, 2019, vol. 74, issue 1, No 10, 195-211

Abstract: Abstract In this paper we extend the notion of minimal solutions for a vector optimization problem considered by Flores-Bazán et al. (J Optim Theory Appl 164:455–478, 2015) to a set-valued optimization problem, with both vector and set solution criteria. Also, we extend the Gerstewitz function proposed by Hernández and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) and use it to scalarize minimal solutions with respect to set criterion. We also provide an existence result of minimal solutions with set criterion. Finally, we investigate links between the minimal solutions with respect to vector criterion and set criterion.

Keywords: Set-valued optimization; Nonlinear scalarization; Generalized Gerstewitz’s function; 54C60; 90C26; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-019-00740-x

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