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Michael
Michael
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Does anyone have an idea how to project onto the ell^{2,1}$\ell^{2,1}$ ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2} \leq 1$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2} \leq 1$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

Does anyone have an idea how to project onto the $\ell^{2,1}$ ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2} \leq 1$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

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Michael
Michael
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Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2}$$$$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2} \leq 1$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2}$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2} \leq 1$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?

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Michael
Michael
  • 41
  • 3

Projection onto $\ell^{2,1}$ ball

Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve $$ u = \arg \min_u \|u-f \|^2 \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2}$$ for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?