Abstract
Let X be a Banach space and f:X /spl rarr/(-/spl infin/, /spl infin/) be a proper and lower semicontinuous function, denoted as S={x /spl isin/ X:f(x)/spl les/0}, ds(x) :=inf{/spl par/x-s/spl par/:s /spl isin/ S}. We say that the system f(x) /spl les/ 0 (or s) has a local (global) error bound if S is nonempty and, for some 0 < /spl mu/ and /spl epsiv/ /spl isin/(0,+/spl infin/) (/spl epsiv/=+/spl infin/), ds(x) /spl les/ /spl mu/f(x)+/spl forall/x /spl isin/ X with f/sub +/(x)</spl epsiv/, where f(x)/sub +/ := max{f(x),0}. We recall the concept of an abstract subdifferential /spl part//sub /spl omega// subdifferential defined by Wu et al. (2001).
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