Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior

Meenakshi Gupta () and Manjari Srivastava ()
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Meenakshi Gupta: University of Delhi
Manjari Srivastava: University of Delhi

Journal of Global Optimization, 2019, vol. 73, issue 2, No 10, 447-463

Abstract: Abstract In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimization problems involving a generalized oriented distance function have been considered. Characterization of u-minimal solutions of (u-SOP) in terms of solutions of these scalar optimization problems have been obtained. Finally, equivalence of well-posedness of (u-SOP) with well-posedness of these scalar optimization problems have been established.

Keywords: Set optimization; Well-posedness; Hausdorff set-convergence; Nonlinear scalarization function; 49J53; 49K40; 90C48 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10898-018-0695-1

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