Mordukhovich derivatives of the set-valued metric projection operator in general Banach spaces

ABSTRACT

In this paper, we investigate the properties and the precise solutions of the Mordukhovich derivatives of the set-valued metric projection operator onto some closed balls in some general Banach spaces. In the Banach space c, we find the properties of Mordukhovich derivatives of the set-valued metric projection operator onto the closed subspace c₀. We show that the metric projection from C[0, 1] to polynomial with degree less than or equal to n is a single-valued mapping. We investigate its Mordukhovich derivatives and G$\hat{\mathrm{a}}$teaux directional derivatives.

KEYWORDS:

• Metric projection
• G$\hat{\mathrm{a}}$teaux directional differentiability
• Fr${\text{e}}^{\mathrm{\prime }}$chet differentiability
• Mordukhovich derivatives
• Chebyshev’s equioscillation theorem

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 47h05
• 46C05
• 49m27
• 65K10
• 90c25

Acknowledgements

The author is very grateful to Professor Boris S. Mordukhovich and Professor Christiane Tammer for their kind communications, valuable suggestions and enthusiastic encouragements in the development stage of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).