Name
Abstract | ||
|---|---|---|
We consider a proper lower semicontinuous function $f$ on a Banach space X with $\lambda=\inf\{f(x):\;x\in X\}-\infty$. Let $\alpha\geq\lambda$ and $S_\alpha=\{x\in X:\; f(x)\leq\alpha\}$. We define the lower derivative of f at the set $S_\alpha$ by $$\underline{D}(f,S_\alpha)=\liminf_{x\rightarrow S_\alpha}\frac{f(x)-\alpha}{dist(x,S_\alpha)},$$ where $x\rightarrow S_\alpha$ 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. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1137/S0363012901389469 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
global weak sharp minima,proper lower semicontinuous function,global weak sharp minimum,abstract linear inequality system,banach space x,banach spaces,various way,banach space | Mathematical optimization,Mathematical analysis,Banach space,Asplund space,Maxima and minima,Regular polygon,Linear inequality,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
41 | 6 | 0363-0129 |
Citations | PageRank | References |
6 | 1.37 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kung Fu Ng | 1 | 311 | 27.85 |
| Xi Yin Zheng | 2 | 236 | 24.17 |