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arXiv · 2406.18377

Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces

Le Van Hien
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Abstract

In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric projection operator onto any closed balls $\mathbb{B}(c,r)$, which has center $c$ in Hilbert space $H$ and with radius $r > 0$. Finally, we give the formula for calculating the graphical derivative of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces.

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Le Van Hien. 2024-06-26. Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces. https://arxiv.org/abs/2406.18377

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