First-Order and Second-Order Conditions for Error Bounds

Authors:
Zili Wu;Jane J. Ye
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
2003

Citing 0
Cited 6

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Abstract

For a lower semicontinuous function f on a Banach space X, we study the existence of a positive scalar $\mu$ such that the distance function dS associated with the solution set S of $f(x)\leq 0$ satisfies \[ d_S(x)\leq \mu \max\{ f(x),0\} \] for each point x in a neighborhood of some point x0 in X with $f(x)f. In a Hilbert space we further present some second-order conditions. We also establish the corresponding results for a system of inequalities, equalities, and an abstract constraint set.