1
vote
0answers
23 views

Optimization that involves inverse operation.

$\newcommand{\diag}{\operatorname{diag}}$ I have the following optimization problem: \begin{align} \mathop{\arg\min}_\beta & \frac{1}{2} a' [ M + \diag( \beta ) \otimes I_d ]^{-1} a + ...
0
votes
2answers
340 views

Transpose of matrix inverse: $(AA^T)^{-1}A^Tb \stackrel{?}{=} (A^TA)^{-1}A^Tb$

Given the matrix equation: $$ x^TA^TA = b^TA $$ I'm trying to find the least squares solution (i.e.; trying to minimize $r=||Ax-b||$). The matrix $A$ is not necessarily symmetric. When I solve it ...
2
votes
0answers
156 views

Optimization problem about large matrices

I'd like to solve the following optimization problem: Find non-negative scalar $a$, $b$, $c$ to minimize $\| (D-(aA+bB+cC+D^{-1})^{-1})y\|^2+2\operatorname{trace}((aA+bB+cC+D^{-1})^{-1})$ where ...
1
vote
0answers
459 views

Efficient Cholesky decomposition of inverse matrix

I want to generate random numbers from a multivariate normal distribution in Matlab. Normally, this is done like: $w = \overline{w} + \text{chol}(\Sigma) \cdot \vec{l}$ But in my case I don't know ...