Abadie's Constraint Qualification, Hoffman's Error Bounds, and Hausdorff Strong Unicity

Bartelt, Martin; Li, W

doi:10.1006/jath.1997.3243

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“…It is known ( [3], Corollary (15)) that when Bf is strongly unique R n is the convex cone generated by…”

Section: Remark 14mentioning

confidence: 98%

Lipschitz continuity and Gateaux differentiability of the best approximation operator in vector-valued Chebyshev approximation

Bartelt

Swetits

2007

Journal of Approximation Theory

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When G is a finite-dimensional Haar subspace of C X, R k , the vector-valued functions (including complex-valued functions when k is 2) from a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C X, R k the best approximation operator satisfies the strong unicity condition of order 2 and a Lipschitz (Hőlder) condition of order 1 2 . This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1 and has a Gateaux derivative on a dense set of functions in C X, R k .

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“…It is known ( [3], Corollary (15)) that when Bf is strongly unique R n is the convex cone generated by…”

Section: Remark 14mentioning

confidence: 98%

Lipschitz continuity and Gateaux differentiability of the best approximation operator in vector-valued Chebyshev approximation

Bartelt

Swetits

2007

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

Exact order of Hoffman’s error bounds for elliptic quadratic inequalities derived from vector-valued Chebyshev approximation

Bartelt

2000

Math. Program.

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Abadie's Constraint Qualification, Hoffman's Error Bounds, and Hausdorff Strong Unicity

Cited by 2 publications

References 21 publications

Lipschitz continuity and Gateaux differentiability of the best approximation operator in vector-valued Chebyshev approximation

Lipschitz continuity and Gateaux differentiability of the best approximation operator in vector-valued Chebyshev approximation

Exact order of Hoffman’s error bounds for elliptic quadratic inequalities derived from vector-valued Chebyshev approximation

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