The Continuity of Metric Projections as Functions of the Data,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1973
- Accession Number
- AD0760041
Entities
People
- James W. Daniel
Organizations
- University of Texas at Austin