I'm not asking for a solution, I just need to know what type of optimization is this problem?. Find $\mathbf{q}$ that minimizes the following: $$\min\_\mathbf{q}{|\mathbf{BXq|^2}}$$ $$\, \mbox{s.t}\ q\_i^Hq\_i=1, i=1,2,...,N$$ $\mathbf{B}$ is given and is $M \times N$, $\mathbf{X}$ is an $N \times N$ diagonal matrix and is given, $\mathbf{q}$ is an $N \times 1$ vector with entries $q\_i$ and $|.|$ denotes the absolute

The objective function can be simplified to: $\mathbf{q^HX^HB^HBXq=q^HGq}$ where $\mathbf{G=X^HB^HBX}$. The opimization problem becomes: $$\min\_\mathbf{q}({\mathbf{q^HGq}})$$ $$\, \mbox{s.t}\ q\_i^Hq\_i=1, i=1,2,...,N$$I would be grateful if someone would let me know what kind of optimization is this problem. Any references would help too.