Abstract
Let C be a fixed compact convex subset of \({\mathbb R}_{++}^{n}\) and let x p be the unique minimal ℓ p -norm element in C for any \(p: \ 1<p<\infty\). In this paper, we study the convergence of x p as p→ ∞ or \(p\searrow 1\), 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.
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Communicated by D. G. Luenberger
The author thanks Professor H. Komiya for valuable advice and an anonymous referee for kind comments.
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Kido, K. Convergence Theorems for ℓ p -Norm Minimizers with Respect to p. J Optim Theory Appl 125, 577–589 (2005). https://doi.org/10.1007/s10957-005-2090-6
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DOI: https://doi.org/10.1007/s10957-005-2090-6