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 x-f11 as x ranges over a polyhedral set C defined by a finite number of real-valued 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