Variational Analysis of Paraconvex Multifunctions

Our aim in this article is to study the class of so-called ρ - paraconvex multifunctions from a Banach space X into the subsets of another Banach space Y . These multifunctions are defined in relation with a modulus function ρ : X → [ 0 , + ∞ ) satisfying some suitable conditions. This class of mult...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 193; H. 1-3; S. 180 - 218
Hauptverfasser: Van Ngai, Huynh, Tron, Nguyen Huu, Van Vu, Nguyen, Théra, Michel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2022
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Cones
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Sum rules
Theory of Computation
Lower
Fréchet subdifferential
functions
Coderivatives
Weak convexity
Paraconvexity
Approximate convex function
90C30
Paramonotonicity
49J53
Fréchet normal cone
49J52
Fuzzy mean value theorem
ISSN:0022-3239, 1573-2878
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Zusammenfassung:Our aim in this article is to study the class of so-called ρ - paraconvex multifunctions from a Banach space X into the subsets of another Banach space Y . These multifunctions are defined in relation with a modulus function ρ : X → [ 0 , + ∞ ) satisfying some suitable conditions. This class of multifunctions generalizes the class of γ - paraconvex multifunctions with γ > 1 introduced and studied by Rolewicz, in the eighties and subsequently studied by A. Jourani and some others authors. We establish some regular properties of graphical tangent and normal cones to paraconvex multifunctions between Banach spaces as well as a sum rule for coderivatives for such class of multifunctions. The use of subdifferential properties of the lower semicontinuous envelope function of the distance function associated to a multifunction established in the present paper plays a key role in this study.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02021-2