Mathematical Programming

, Volume 104, Issue 2, pp 329–346

Metric regularity of semi-infinite constraint systems

  • M.J. Cánovas
  • A.L. Dontchev
  • M.A. López
  • J. Parra
Article

DOI: 10.1007/s10107-005-0618-z

Cite this article as:
Cánovas, M., Dontchev, A., López, M. et al. Math. Program. (2005) 104: 329. doi:10.1007/s10107-005-0618-z

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.

Keywords

Semi-infinite programming Metric regularity Distance to inconsistency Conditioning 

Mathematics Subject Classification (1991)

90C34 49J53 49K40 65Y20 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M.J. Cánovas
    • 1
  • A.L. Dontchev
    • 2
  • M.A. López
    • 3
  • J. Parra
    • 1
  1. 1.Operations Research CenterMiguel Hernández University of ElcheElche (Alicante)Spain
  2. 2.Mathematical ReviewsAnn ArborUSA
  3. 3.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain