ISSN:
1436-4646
Keywords:
Mathematics Subject Classification (1991): 90C31, 41A50, 90C47
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. In this paper, we introduce the exact order of Hoffman’s error bounds for approximate solutions of elliptic quadratic inequalities. Elliptic quadratic inequalities are closely related to Chebyshev approximation of vector-valued functions (including complex-valued functions). The set of Chebyshev approximations of a vector-valued function defined on a finite set is shown to be Hausdorff strongly unique of order exactly 2 s for some nonnegative integer s. As a consequence, the exact order of Hoffman’s error bounds for approximate solutions of elliptic quadratic inequalities is exactly 2 -s for some nonnegative integer s. The integer s, called the order of deficiency (which is computable), quantifies how much the Abadie constraint qualification is violated by the elliptic quadratic inequalities.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s101070050015
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