Authors

Citation

M. Gugat, Error bounds for infinite systems of convex inequalities without Slater's condition, MATH PROGR, 88(2), 2000, pp. 255-275

Citations number

23

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Mathematics

Journal title

MATHEMATICAL PROGRAMMING

ISSN journal

0025-5610
→ ACNP

Volume

88

Issue

2

Year of publication

2000

Pages

255 - 275

Database

ISI

SICI code

0025-5610(200008)88:2<255:EBFISO>2.0.ZU;2-M

Abstract

The feasible set of a convex semi-infinite program is described by a possib
ly infinite system of convex inequality constraints. We want to obtain an u
pper bound for the distance of a given point from this set in terms of a co
nstant multiplied by the value of the maximally violated constraint functio
n in this point. Apart from this Lipschitz case we also consider error boun
ds of Holder type, where the value of the residual of the constraints is ra
ised to a certain power.
We give sufficient conditions for the validity of such bounds, Our conditio
ns do not require that the Slater condition is valid. For the definition of
our conditions, we consider the projections on enlarged sets corresponding
to relaxed constraints. We present a condition in terms of projection mult
ipliers. a condition in terms of Slater points and a condition in terms of
descent directions. For the Lipschitz case, we give five equivalent charact
erizations of the validity of a global error bound.
We extend previous results in two directions: First, we consider infinite s
ystems of inequalities instead of finite systems, The second point is that
we do not assume that the Slater condition holds which has been required in
almost all earlier papers.