English

Frechet differentiability of the metric projection operator in Banach spaces

Functional Analysis 2024-01-04 v1

Abstract

In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and convex subsets, we find the exact expressions for Frechet derivatives and Gateaux directional derivatives of the metric projection operator.

Keywords

Cite

@article{arxiv.2401.01480,
  title  = {Frechet differentiability of the metric projection operator in Banach spaces},
  author = {Jinlu Li},
  journal= {arXiv preprint arXiv:2401.01480},
  year   = {2024}
}

Comments

37 pages. arXiv admin note: substantial text overlap with arXiv:2312.14362