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The research project focuses on set-optimization problems, as recently studied. The activity will be addressed, but not restricted to:
1.Necessary and sufficient optimality conditions in set-optimization via directional derivatives;
2.Calculus for set-valued maps in conlinear spaces;
3.Approximate solutions for set-optimization problems and well-posedness;
4.Applications to vector optimization as a special case of set-optimization.
Some duality theory, developed for set-optimization has been successfully applied to the theory of set-valued risk measures. The set-valued formulation of existing scalar and vector risk measures will eventually be studied in the project.
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