0

I have a matrix optimization problem denoted as below:
$$\arg\min_{\alpha_i, \beta_i} \lVert \sum_{i=1}^4 (\alpha_i M_i - \beta_i P_i) \rVert^2_2 \\ \text{s.t. } \alpha_i > 0, \beta_i > 0$$
where $M_i,i=1,2,3,4$ and $P_i,i=1,2,3,4$ are constant square matrices in the same shape, and $\lVert \cdot \rVert_2^2$ is $l_2$ norm of matrix. Find the parameters $\alpha_i, i=1,2,3,4$ and $\beta_i, i=1,2,3,4$ that minimize the formula above.

Johnachale
  • 39
  • 2
    As written, $\alpha_i\to 0+,\beta_i\to 0+$ is a minimizing sequence (though it may happen that the infimum of $0$ is attained in the domain as well). Apparently something more interesting was meant... – fedja Feb 10 '22 at 01:43
  • 1
    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Feb 10 '22 at 01:49

0 Answers0