Abstract
Let C be a fixed compact convex subset of ℝ++ and let x p be the unique minimal lp-norm element in C for any p: \ 1<p<\∞. In this paper, we study the convergence of x p as p→ ∞ or p ↘ 1, respectively. We characterize also the limit point as the minimal element of C with respect to the lexical minimax order relation or the lexical minitotal order relation, respectively.
Original language | English |
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Pages (from-to) | 577-589 |
Number of pages | 13 |
Journal | Journal of Optimization Theory and Applications |
Volume | 125 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2005 Jun |
Externally published | Yes |
Keywords
- Approximations
- Lexicographical orders
- Minimum-norm problems
- l-norm
ASJC Scopus subject areas
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics