I have an optimization problem of the following form:

Min $\|Qa-b\|$ st. $Q \succeq 0$ where $a,b \in \mathbb{R}^n$ are given and the square matrix $Q$ is the variable. It is most probably a semidefinite programming problem. Is there a standard answer to this problem ? If not, which algorithm is best suited to solve this problem ?

I have an optimization problem of the following form

$$\text{minimize} \,\|Qa-b\|_2 \quad \text{ subject to } Q \succeq 0$$

where $a,b \in \mathbb{R}^n$ are given and the $n \times n$ square matrix $Q$ is the variable.

• It is most probably a semidefinite programming problem. Is there a standard answer to this problem?

• If not, which algorithm is best suited to solve this problem?