Tuesday, 13:15 - 13:40 h, Room: H 2051

 

Marius Durea
Metric regularity and Fermat rules in set-valued optimization

 

Abstract:
We discuss several techniques for getting Fermat rules for set-valued unconstrained optimization. Among these techniques which are, in a sense, equivalent, we focus on a method based on the incompatibility between the metric regularity (or openness at linear rate) of set-valued maps and the optimality in the sense of Pareto. We describe technically how the well known contradiction between regularity and optimality could be successfully transposed into a set-valued context and then we identify several metric regularity/ openness results which serve our final purpose. We observe that in order to get good Fermat rules (i.e. under mild conditions) one should have to derive new specific openness results which could be of interest for its own. Several possibilities in this direction are investigated, each one giving a specific final outcome. Moreover, some applications to vector equilibrium problems are envisaged.
Since, in general, our method allows to firstly deduce approximate Fermat rules for set-valued optimization problems in the setting of general Banach spaces, through this presentation we will have the possibility to underline several regularity and stability issues.

 

Talk 1 of the invited session Tue.2.H 2051
"Regularity and sensitivity in multicriteria optimization" [...]
Cluster 24
"Variational analysis" [...]

 

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