Timeline for On the convergence of a special fixed point iteration
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2011 at 21:03 | comment | added | Brian Borchers | No, it's not gradient ascent- it's "projected gradient ascent." Look for information on "projected gradient descent" methods for minimization problems- the convergence of the projected gradient descent method is standard textbook material. | |
| Dec 11, 2011 at 19:41 | comment | added | Antoine Levitt | In general, the way to prove such statement is with the Banach fixed point theorem. Have you tried it? | |
| Dec 11, 2011 at 18:33 | comment | added | Guoxin Zhang | It seems not a standard gradient ascent algorithm. Can anyone give some hints? Thanks. | |
| Dec 11, 2011 at 17:58 | comment | added | Guoxin Zhang | hi, thanks for the quick reply. It's should be $\frac{1}{2}x^TQx+d^Tx$ I've corrected it. d is also nonnegative, and I've mentioned that in the beginning. | |
| Dec 11, 2011 at 17:55 | history | edited | Guoxin Zhang | CC BY-SA 3.0 |
added 11 characters in body
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| Dec 11, 2011 at 17:37 | comment | added | Brian Borchers | You haven't described any projection onto the nonnegative orthant- I assume that you're doing that. Although Q is nonnegative, it's conceivable that negative elements in d could cause the iteration to to move outside of the nonnegative orthant. If you used $y_{n+1}=2Qx_{n}+d$, then you'd have a projected gradient ascent algorithm for which there are plenty of convergence results. | |
| Dec 11, 2011 at 16:54 | comment | added | Guoxin Zhang | In short, the problem is actually: maximize a quadratic form (with positive coefficients) on the direct project of some unit spheres | |
| Dec 11, 2011 at 16:36 | history | asked | Guoxin Zhang | CC BY-SA 3.0 |