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- W1979185698 abstract "We consider a proper lower semicontinuous function $f$ on a Banach space X with $lambda=inf{f(x):;xin X}>-infty$. Let $alphageqlambda$ and $S_alpha={xin X:; f(x)leqalpha}$. We define the lower derivative of f at the set $S_alpha$ by $$underline{D}(f,S_alpha)=liminf_{xrightarrow S_alpha}frac{f(x)-alpha}{dist(x,S_alpha)},$$ where $xrightarrow S_alpha$ can be interpreted in various ways. We show that, when f is convex and $alpha = lambda$, it is equal to the largest weak sharp minima constant. In terms of these derivatives and subdifferentials, we present several characterizations for convex f to have global weak sharp minima. Some of these results are also shown to be valid for nonconvex f. As applications, we give error bound results for abstract linear inequality systems." @default.
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- W1979185698 date "2003-01-01" @default.
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- W1979185698 title "Global Weak Sharp Minima on Banach Spaces" @default.
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- W1979185698 doi "https://doi.org/10.1137/s0363012901389469" @default.
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