English

Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces

Functional Analysis 2024-05-03 v2

Abstract

In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces. We find the exact expressions for Frechet derivatives. Since Frechet differentiability implies Gateaux directional differentiability, the results obtained in this paper strengthen the results obtained in [8] and [10] about the directional differentiability of the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in the real Hilbert space l2.

Keywords

Cite

@article{arxiv.2312.14362,
  title  = {Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces},
  author = {Jinlu Li},
  journal= {arXiv preprint arXiv:2312.14362},
  year   = {2024}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2311.16310