Find extrema of quadratic problem

94 Views Asked by At

I have to find the extrema of the following function:

$f(x) = x'Hx + c'x$,

where $x'$ means the transpose. Moreover, $x,c \in \Re^n$ and $H \in \Re^{nxn}$. The matrix $H$ does not have any special property.

If I consider it as a function, I can compute the gradient and set it equal to zero:

$x = -(H+H')^{-1}c$,

and this is the (vector of?) stationary point. But how do I procede further? I can compute the Hessian ($H+H'$), but then? Thank you.