期刊論文
| 學年 | 73 |
|---|---|
| 學期 | 1 |
| 出版（發表）日期 | 1985-01-01 |
| 作品名稱 | On the daulity operator of a convex cone |
| 作品名稱（其他語言） | |
| 著者 | Tam, Bit-shun |
| 單位 | 淡江大學數學學系 |
| 出版者 | New York : Elsevier Inc. |
| 著錄名稱、卷期、頁數 | Linear Algebra and Its Applications 64, pp.33-56 |
| 摘要 | Let C be a convex set in Rn. For each yϵC, the cone of C at y, denoted by cone(y, C), is the cone {α(x − y): α ⪖ 0 and xϵC}. If K is a cone in Rn, we shall denote by K∗ its dual cone and by F(K) the lattice of faces of K. Then the duality operator of K is the mapping View the MathML source given by View the MathML source. Properties of the duality operator dK of a closed, pointed, full cone K have been studied before. In this paper, we study dK for a general cone K, especially in relation to dcone(y, K), where yϵK. Our main result says that, for any closed cone K in Rn, the duality operator dK is injective (surjective) if and only if the duality operator dcone(y, K) is injective (surjective) for each vector yϵK ∼ [K ∩ (− K)]. In the last part of the paper, we obtain some partial results on the problem of constructing a compact convex set C, which contains the zero vector, such that cone (0, C) is equal to a given cone. |
| 關鍵字 | |
| 語言 | en |
| ISSN | 0024-3795 1873-1856 |
| 期刊性質 | 國外 |
| 收錄於 | SCI |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | |
| 國別 | USA |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41404 ) |