Invited Session Tue.2.H 2051

Tuesday, 13:15 - 14:45 h, Room: H 2051

Cluster 24: Variational analysis [...]

Regularity and sensitivity in multicriteria optimization

 

Chair: Constantin Zalinescu

 

 

Tuesday, 13:15 - 13:40 h, Room: H 2051, Talk 1

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.

 

 

Tuesday, 13:45 - 14:10 h, Room: H 2051, Talk 2

Radu Strugariu
Metric regularity and subregularity of set-valued mappings with applications to vector optimization

 

Abstract:
This presentation is devoted to the investigation of different types of regularity for set-valued mappings, with applications to the study of the well-posedness of the solution mappings associated to parametric variational systems. We present some general theorems concerning chain rules for linear openness of multifunctions and we obtain, as particular cases, some classical and also some new results in this field of research, including the celebrated Lyusternik Graves Theorem. Also, we classify the at-point regularities (or subregularities) of set-valued mappings into two categories and then we analyze their relationship. After that, we show how to use the subregularity properties to deduce implicit theorems for set-valued maps. Finally, we present some applications to the study of multicriteria optimization problems.

 

 

Tuesday, 14:15 - 14:40 h, Room: H 2051, Talk 3

Constantin Zalinescu
Variational principles for multifunctions and applications

 

Abstract:
The usefulness of the Ekeland Variational Principle (EVP) is well known in Nonlinear Analysis. In the last thirty years many variants for vector-valued functions were established. In our talk we present several versions of the EVP in which the usual (minorized) function as well as the distance function are replaced by multifunctions.
Then we present an application to error bounds.

 

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