
Accession Number : AD0760041
Title : The Continuity of Metric Projections as Functions of the Data,
Corporate Author : TEXAS UNIV AUSTIN CENTER FOR NUMERICAL ANALYSIS
Personal Author(s) : Daniel,James W.
Report Date : APR 1973
Pagination or Media Count : 11
Abstract : Let X be a Hilbert space, and consider the point (x sub 0) minimizing, for a given f in X, the distance 11 xf11 as x ranges over a polyhedral set C defined by a finite number of realvalued equalities and inequalities. The author wishes to see how (x sub 0) varies when (y sub 0) and C vary. It is easy to see that (x sub 0) is Holder continuous with exponent 1/2 in its dependence on these parameters; this estimate is in general sharp. It is shown, however, that in certain cases (x sub 0) is actually Lipschitz continuous in its dependence on the parameters which are used to define the set C. (Author)
Descriptors : (*FUNCTIONAL ANALYSIS, INEQUALITIES), CONVEX SETS, HILBERT SPACE, QUADRATIC PROGRAMMING, MATRICES(MATHEMATICS), THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE