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- W3100148974 abstract "In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker concept of minimizers and weaker variational inequalities. The implications are proved using scalarization techniques that eventually provide original problems, not fully equivalent to the set-valued counterparts. Therefore, we try, in the course of this note, to close the network among the various notions proposed. More specifically, we prove that a minimizer is always a weak minimizer, and a solution to the stronger variational inequality always also a solution to the weak variational inequality of the same type. As a special case we obtain a complete characterization of efficiency and weak efficiency in vector optimization by set-valued variational inequalities and their scalarizations. Indeed this might eventually prove the usefulness of the set-optimization approach to renew the study of vector optimization." @default.
- W3100148974 created "2020-11-23" @default.
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- W3100148974 date "2016-06-01" @default.
- W3100148974 modified "2023-10-14" @default.
- W3100148974 title "Weak minimizers, minimizers and variational inequalities for set-valued functions. A blooming wreath?" @default.
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- W3100148974 doi "https://doi.org/10.1080/02331934.2016.1189550" @default.
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