A Note on Error Bounds for Convex and Nonconvex Programs

Authors:
Dimitri P. Bertsekas
Affiliations:
Department of Electrical Engineering and Computer Science, M.I.T., Cambridge, MA, 02139. bertsekas@LIDS.MIT.EDU
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Year:
1999

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Abstract

Given a single feasible solution x_F and a single infeasible solution x_I of a mathematical program, weprovide an upper bound to the optimal dual value. We assume that x_Fsatisfies a weakened form of the Slatercondition. We apply the bound to convex programs and we discuss itsrelation to Hoffman-like bounds. As a special case, we recover a bounddue to Mangasarian [11] on the distance of a point to a convex setspecified by inequalities.