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#3) For a convex set S C R", what is the normal cone Ng(x) of S at a point x E S? Consider S := B := {() : d.Ns (₁²). Find Ns 1151} : max {[x], [y]} ≤ 1

#3) For a convex set S C R", what is the normal cone Ng(x) of S at a point x E S? Consider S := B := {() : d.Ns (₁²). Find Ns 1151} : max {[x], [y]} ≤ 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For a convex set \( S \subseteq \mathbb{R}^n \), what is the normal cone \( \mathcal{N}_S(x) \) of \( S \) at a point \( x \in S \)? Consider \( S := \overline{B}_\infty := \left\{ \begin{pmatrix} x \\ y \end{pmatrix} : \max \{|x|, |y|\} \leq 1 \right\} \). Find \( \mathcal{N}_S \begin{pmatrix} -1 \\ 1 \end{pmatrix} \).
Transcribed Image Text:For a convex set \( S \subseteq \mathbb{R}^n \), what is the normal cone \( \mathcal{N}_S(x) \) of \( S \) at a point \( x \in S \)? Consider \( S := \overline{B}_\infty := \left\{ \begin{pmatrix} x \\ y \end{pmatrix} : \max \{|x|, |y|\} \leq 1 \right\} \). Find \( \mathcal{N}_S \begin{pmatrix} -1 \\ 1 \end{pmatrix} \).
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