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For a positive semi-definite matrix $C$, I want to find the solution to the following problem:

$\arg\max_{h\geq 0} h^T C h\quad$ s.t. $\quad h^T h\leq 1$

Any pointers are welcome.

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The magic words are quadratically constrained quadratic programming. And semidefinite programming.

EDIT I misread the question (it is a convex maximization problem). This is still somewhat tractable in practice (since the objective still has convex epigraphs), but see the excellent answer by @NoahStein to this question.

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  • $\begingroup$ ghostbusters.wikia.com/wiki/The_Magic_Word $\endgroup$
    – Will Jagy
    Commented Oct 17, 2013 at 20:14
  • $\begingroup$ please note this is a maximization problem so cannot be mapped to a QCQP $\endgroup$
    – Abhishek Kumar
    Commented Oct 17, 2013 at 22:26
  • $\begingroup$ @AbhishekKumar oops, misread the question. See the edit. $\endgroup$
    – Igor Rivin
    Commented Oct 18, 2013 at 2:01

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