A unified minimal solution in set optimization
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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.
KeywordsSet-valued optimization Nonlinear scalarization Generalized Gerstewitz’s function
Mathematics Subject Classification54C60 90C26 90C29 90C31
The authors wish to thank referee and associate editor for their suggestions which helped to improve the presentation of this article. This research, for the second author, was supported by MATRIC scheme of Department of Science and Technology, India.
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