Covering constants for metric projection operator with applications to stochastic fixed-point problems

The theory of generalized differentiation in set-valued analysis is based on Mordukhovich derivative (Mordukhovich coderivative), which has been widely applied to optimization theory, equilibrium theory, variational analysis, with respect to set-valued mappings. In this paper, we use the Mordukhovic...

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Vydáno v:Journal of global optimization Ročník 92; číslo 4; s. 993 - 1020
Hlavní autor: Li, Jinlu
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2025
Springer Nature B.V
Témata:
Banach spaces
Closed balls
Computer Science
Fixed points (mathematics)
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Real Functions
Theorems
Metric projection
90C31
47H10
Fréchet differentiability
Mordukhovich derivative
49J53
49J52
Stochastic fixed-point
Locally and globally stochastic fixed-point variable
Covering constant
ISSN:0925-5001, 1573-2916
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Shrnutí:The theory of generalized differentiation in set-valued analysis is based on Mordukhovich derivative (Mordukhovich coderivative), which has been widely applied to optimization theory, equilibrium theory, variational analysis, with respect to set-valued mappings. In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for metric projection onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. This is considered as optimizing the metric projection with respect to covering values. We study three cases: closed balls in uniformly convex and uniformly smooth Banach spaces, closed and convex cylinders in l p and positive cones in L p , for some p with 1 <  p  <  ∞ . By Arutyunov Mordukhovich and Zhukovskiy Parameterized Coincidence Point Theorem (Theorem 3.1 in (J Optim Theory Appl 196:177–198, 2023)), which is simply called Arutyunov Mordukhovich Zhukovskiy Theorem, and as applications of covering constants obtained in this paper, we prove solvability of some locally stochastic fixed-point problems. We also provide three examples with specific solutions of both locally and globally stochastic fixed-point problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-025-01501-9