Name
Title | ||
|---|---|---|
Convergence of the Associated Sequence of Normal Cones of a Mosco Convergent Sequence of Sets. |
Abstract | ||
|---|---|---|
In 1977, Attouch established a relationship between the Mosco epiconvergence of a sequence of convex functions and the graph convergence of the associated sequence of subdifferentials, which has been found to have many important applications in optimization. In 1995, Levy, Poliquin, and Thibault proved Attouch-type theorems for a sequence of primal-lower-nice (not necessarily convex) functions with variational behavior of "order two." In this paper, using the proximal analysis technique, we provide convergence results on the associated sequence of normal cones of a Mosco-convergent sequence of general closed sets. Under the uniform subsmoothness assumption, some sharper convergence results are established. As applications, we establish Attouch-type theorems for a sequence of more general quasi-subsmooth functions with variational behavior of "order one." |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/110851158 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
Mosco convergence,epigraph convergence,normal cone,subdifferential,subsmoothness | Discrete mathematics,Mathematical optimization,Weak convergence,Combinatorics,Normal convergence,Limit of a sequence,Mosco convergence,Compact convergence,Subderivative,Convergence tests,Mathematics,Modes of convergence | Journal |
Volume | Issue | ISSN |
22 | 3 | 1052-6234 |
Citations | PageRank | References |
2 | 0.65 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xi Yin Zheng | 1 | 236 | 24.17 |
| Zhou Wei | 2 | 37 | 2.73 |