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

Jinlu Li ()
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Jinlu Li: Shawnee State University

Journal of Global Optimization, 2025, vol. 92, issue 4, No 7, 993-1020

Abstract: Abstract 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 lp and positive cones in Lp, for some p with 1

Keywords: Metric projection; Fréchet differentiability; Mordukhovich derivative; Covering constant; Stochastic fixed-point; Locally and globally stochastic fixed-point variable; 49J52; 49J53; 47H10; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01501-9

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