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How to solve Rayleigh Quotient type problem?

$$\max (w+w_0)^tC(w+w_0) \text{ s.t. } w'w=1,$$

where $w_0$ is given.

Thank you!

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2  
What do you know about $C$? – Davide Giraudo Apr 19 '12 at 14:40
    
real, symmetrical, but maynot be PSD... – Luna Apr 19 '12 at 20:11
    
Have you worked in the case $C$ diagonal? – Davide Giraudo Apr 19 '12 at 20:23
    
How to solve that case? Could you please elaborate? Thank you! – Luna Apr 20 '12 at 2:14
    
Did you try with Lagrange multiplier? I guess it will work. – Davide Giraudo Apr 20 '12 at 9:04

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