Quadratic optimization


(palas) #1

My minimization problem has objective function in x^TQx form, where x is unknown and Q is given positive definite matrix. It is quadratic, and is not in linear matrix form. But surprisingly cvx toolbox is giving a solution. how can it be possible?
The optimization problem is as follows:

Minimize x^TQx
subject to f(x)<=0
where Q=Q^T>0 is given and f(x) is in LMI form.


(Mark L. Stone) #2

If x is a vector, this is a convex quadratic, which can be minimized, all in accordance with CVX’s rules. http://cvxr.com/cvx/doc/dcp.html#scalar-quadratic-forms

x'*Q*x and quad_form(x,Q) are both allowed and are equivalent.