Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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Solving a matrix equation using numerical optimization

To my knowledge, if $A \in \mathbf{S}^n_{++}$, then given any $b \in \mathbb{R}^n$, the system of linear equations $Ax = b$ has a unique solution $x^* \in \mathbb{R}^n$. Moreover, the solution $x^* ...