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Zbl 1072.41019
Jeyakumar, V.; Mohebi, H.
A global approach to nonlinearly constrained best approximation. (English)
[J] Numer. Funct. Anal. Optimization 26, No. 2, 205-227 (2005). ISSN 0163-0563; ISSN 1532-2467/e

Linearly and nonlinearly constrained problems of best approximation in a Hilbert space are discussed in this article. For instance, characterizations of best dual approximations are provided and a perturbation theory of approximation problems with cone-convex constraints is developed. For the linearly constrained case, it is shown that the work carried out in this paper is a generalization of the linear case. Several examples are given to illustrate the results.
[Martin D. Buhmann (Giessen)]

MSC 2000:: *41A65 Abstract approximation theory
41A29 Approximation with constraints
90C30 Nonlinear programming

Keywords: best constrained approximation; bounded linear regularity; cone-convex constraints; dual constraint qualifications; global conditions; Slater's condition; strong conical hull intersection property

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