Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is the dual of a norm that is the sum of two-norms? Specifically, say we have the following norm for a $\mathbf{x}\in \mathbb{R}^n$ and $\mathbf{A}_i \in \mathbb{R}^{m \times n}$

$\|\mathbf{x}\| = \displaystyle{ \sum_{i=0}^{n} \|\mathbf{A}_i \cdot \mathbf{x} \|_2}$.

How would you then find

$\|\mathbf{y}\|_* = \underset{\mathbf{x}}{\mathrm{max}} \left\{ |\mathbf{y}^T \cdot \mathbf{x}| \;\; \mathrm{s.t.} \;\; \|\mathbf{x}\| \leq 1\right\}$?

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.