Metric regularity of semi-infinite constraint systems |
| |
| Authors: | MJ Cánovas AL Dontchev MA López J Parra |
| |
| Institution: | (1) Operations Research Center, Miguel Hernández University of Elche, 03202 Elche (Alicante), Spain;(2) Mathematical Reviews, Ann Arbor, MI 48107-8604, USA;(3) Department of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain |
| |
| Abstract: | We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and
inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings:
given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F+g is not metrically regular is equal to the reciprocal to the modulus of regularity of F. The Lyusternik-Graves theorem gives a straightforward extension of these results to nonlinear systems. We also discuss the
distance to infeasibility for homogeneous semi-infinite linear inequality systems.
Dedicated to R. T. Rockafellar on his 70th Birthday
Research partially supported by grants BFM2002-04114-C02 (01-02) from MCYT (Spain) and FEDER (E.U.), GV04B-648 and GRUPOS04/79
from Generalitat Valenciana (Spain), and Bancaja-UMH (Spain). |
| |
| Keywords: | Semi-infinite programming Metric regularity Distance to inconsistency Conditioning |
| 本文献已被 SpringerLink 等数据库收录！ |
|
