Approximate Solutions and Levitin–Polyak Well-Posedness for Set Optimization Using Weak Efficiency

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

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 10, 208 pages

Abstract: Abstract The present study is devoted to define a new notion of approximate weak minimal solution based on a set order relation introduced by Karaman et al. (Positivity 22(3):783–802, 2018) for a constrained set optimization problem. Sufficient conditions have been found for the closedness of minimal solution sets. Using the Painlevé–Kuratowski convergence, the stability aspects of the approximate weak minimal solution sets are discussed. Further, a notion of Levitin–Polyak well-posedness for the set optimization problem is introduced. Sufficiency criteria and some characterizations of the above defined well-posedness are established. An alternative approach to obtain robust solutions for uncertain vector optimization problems is discussed as an application.

Keywords: Set optimization; Approximate solution; Stability; Well-posedness; Set convergence; Robust optimization; 49K40; 49J53; 90C31; 90C48 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01683-0

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