0
votes
1answer
67 views

Extremum of a multidimensional quadratic function

I have the following function: $$ g(h) = h'\Sigma\Sigma'h-h'm-r, $$ where $h$ is a vector in $\mathbb{R}^M$, $\Sigma$ is a $M\times K$ matrix such that $\Sigma\Sigma'$ is positive definite and has ...
2
votes
1answer
153 views

A question regarding local minimizer of a function restricted on a circle

I have a quadratic function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, $f(\mathbf{x}) = (\mathbf{x}-\mathbf{p})^\top \mathbf{Q} (\mathbf{x} - \mathbf{p})$ where $\mathbf{Q}$ is positive definite and ...
8
votes
4answers
2k views

Determining if a quadratic is always positive

Is there a quick and systematic method to find out if a quadratic equation is always positive or may have positive and negative or always negative for all values to its variables? Say for a quadratic ...