Unconstrained optimization problem (lasso with modification)

Asked Jul 22 '14 at 20:40

Active Jul 22 '14 at 20:40

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I am looking to solve the following unconstrained optimization problem:

$$\arg \min_U \|b-A(UY^*)\|_F^2+\lambda\|U\|_1$$

where $\|.\|_F$ is frobenius norm.

I know that the solution without the $\lambda\|U\|_1$ term, will be the least square problem in the form of $AUY^* = b$. How can I solve this problem considering the sparsity constraint.

asked Jul 22 '14 at 20:40

Parisa

Does it help to write $|U|1 = \max_j \sum_i |[U]{ij}|$? – copper.hat Jul 22 '14 at 20:47
Here's a related question. – littleO Jul 22 '14 at 20:58

Unconstrained optimization problem (lasso with modification)

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