Abstract | ||
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The paper is devoted to studying the lower semicontinuity of vector-valued mappings. The main object under consideration is the lower limit. We first introduce a new definition of an adequate concept of lower and upper level sets and establish some of their topological and geometrical properties. A characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define a concept of vector lower limit, proving its lower semicontinuity, and furnishing in this way a concept of lower semicontinuous regularization for mappings taking their values in a complete lattice. The results obtained in the present work subsume the standard ones when the target space is finite dimensional. In particular, we recapture the scalar case with a new flexible proof. In addition, extensions of usual operations of lower and upper limits for vector-valued mappings are explored. The main result is finally applied to obtain a continuous D.C. decomposition of continuous D.C. mappings. |
Year | DOI | Venue |
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2006 | 10.1007/s10898-005-3839-z | JOURNAL OF GLOBAL OPTIMIZATION |
Keywords | Field | DocType |
DC-mappings,lower level set,lower semicontinuous regularization,vector lower limit,vector-valued mappings | Mathematical optimization,Mathematical analysis,Scalar (physics),Level set,Regularization (mathematics),Complete lattice,Mathematics | Journal |
Volume | Issue | ISSN |
35.0 | 2 | 0925-5001 |
Citations | PageRank | References |
3 | 0.81 | 0 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
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Mohamed Ait Mansour | 1 | 12 | 2.59 |
A. Metrane | 2 | 75 | 5.75 |
Michel Théra | 3 | 122 | 13.95 |