Abstract
Let C be a fixed compact convex subset of \({\mathbb R}_{++}^{n}\) and let xp be the unique minimal lp-norm element in C for any \(p: \ 1<p<\infty\). In this paper, we study the convergence of xp 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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