Best Approximation and Perturbation Property in Hilbert Spaces

Y. R. He and K. F. Ng
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Y. R. He: Sichuan Normal University
K. F. Ng: Chinese University of Hong Kong

Journal of Optimization Theory and Applications, 2005, vol. 126, issue 2, No 3, 265-285

Abstract: Abstract We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.

Keywords: Best approximation; abstract nonlinear systems; strong conical hull intersection property; Robinson constraint qualification (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-4714-2

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