Directional derivatives and subdifferentials for set-valued maps applied to set optimization

Marius Durea () and Radu Strugariu ()
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Marius Durea: Alexandru Ioan Cuza University
Radu Strugariu: Gh. Asachi Technical University

Journal of Global Optimization, 2023, vol. 85, issue 3, No 7, 687-707

Abstract: Abstract We present a general method to devise directional derivatives and subdifferentials for set-valued maps that generalize the corresponding constructions from the classical situation of real-valued functions. We show that these generalized differentiation objects enjoy some properties that, on the one hand, meaningfully extend the aforementioned case and, on the another hand, are useful to deal with the so-called $$\ell $$ ℓ -minimality in set optimization problems.

Keywords: Set optimization; Generalized directional derivatives; Subdifferentials of set-valued maps; Optimality conditions; Penalization methods; 54C60; 46G05; 90C46 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01222-3

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