Maximize the quadratic form by choosing appropriate matrix

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What is the usual term/method for the functional optimization problem $$max_{Q\in\mathbb{S}_n}\quad x'Qx$$ with the constraint $x'x=1$ OR $x'1=$some constant? Notice that the maximizer should be a $n\times n$ matrix $Q\in\mathbb{S}_{n}$ whose entries are 0 or 1.