caa a22 4500 475769791 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/s101070050015 doi (NATIONALLICENCE)springer-10.1007/s101070050015 Exact order of Hoffman's error bounds for elliptic quadratic inequalities derived from vector-valued Chebyshev approximation [Elektronische Daten] [Martin Bartelt, Wu Li] 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. Springer-Verlag Berlin Heidelberg, 2000 Mathematics Subject Classification (1991): 90C31, 41A50, 90C47 nationallicence Bartelt Martin Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA, e-mail: mbartelt@pcs.cnu.edu, US aut Li Wu Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA, e-mail: wli@odu.edu, US aut Mathematical Programming Springer-Verlag 88/2(2000-08-01), 223-253 0025-5610 88:2<223 2000 88 10107 https://doi.org/10.1007/s101070050015 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s101070050015 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bartelt Martin Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA, e-mail: mbartelt@pcs.cnu.edu, US aut NATIONALLICENCE 700 1- Li Wu Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA, e-mail: wli@odu.edu, US aut NATIONALLICENCE 773 0- Mathematical Programming Springer-Verlag 88/2(2000-08-01), 223-253 0025-5610 88:2<223 2000 88 10107 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer