1
$\begingroup$

How can I think of an optimization problem with a matrix variable, as an equivalent optimization problem jointly over the rows of that matrix?

Edit: A sample problem taken from a textbook:

$\underset{X}{\min} \textbf{Tr}(SX) - \log\det X + \lambda||X||_1 \;\; \text{s.t.} \;\; X \in \boldsymbol{S}^n_{++}$

where $\boldsymbol{S}^n_{++}$ is the set of symmetric positive definite $n \times n$ matrices.

  • 0
    Yes. Or as one big vector. – 2017-01-26
  • 0
    Im having trouble thinking of encoding matrix constraints as vector constraints – 2017-01-26
  • 0
    You might want to give an example of what you are talking about otherwise it is impossible to understand the difficulty... – 2017-01-26
  • 0
    @copper.hat I've added a sample problem – 2017-01-26
  • 0
    I'm not exactly sure what you are trying to do. The map $f(x_1,...,x_n) = \begin{bmatrix} x_1 \cdots x_n \end{bmatrix}$ relates the columns to the matrix, so the above can be expressed in that sense. So, I am guessing I am missing the point of your question. – 2017-01-26
  • 0
    I guess the most simple version of my question, is how can I write that optimization problem as $\underset{x_1,\ldots,x_n}{\min}$ – 2017-01-26

0 Answers 0