A note on error bounds for convex and nonconvex programs

Authors
Bertsekas, DP
Citation
Dp. Bertsekas, A note on error bounds for convex and nonconvex programs, COMPUT OP A, 12(1-3), 1999, pp. 41-51
Citations number
13
Categorie Soggetti
Engineering Mathematics
Journal title
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN journal
09266003 → ACNP
Volume
12
Issue
1-3
Year of publication
1999
Pages
41 - 51
Database
ISI
SICI code
0926-6003(199901)12:1-3<41:ANOEBF>2.0.ZU;2-5
Abstract
Given a single feasible solution x(F) and a single infeasible solution x(I) of a mathematical program, we provide an upper bound to the optimal dual v alue. We assume that x(F) satisfies a weakened form of the Slater condition . We apply the bound to convex programs and we discuss its relation to Hoff man-like bounds. As a special case, we recover a bound due to Mangasarian [ 11] on the distance of a point to a convex set specified by inequalities.