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I faced a non-convex optimization problem with unit norm constraint.

I can solve the problem using the gradient descent method and the projection of the gradient onto the tangent plane as in @joriki comment in Gradient Descent with constraints.

The results are very good. Therefore, I want a reference including this method to cite it in my work. Can anyone help?

Community
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Unknown
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You can cite a standard nonlinear programming textbook such as Nocedal and Wright, Bertsekas or Bazaraa, Sherali and Shetty. I think all of them have references to the projected gradient method. You should of course go over and make sure you're citing the right section.

ps: You might also want to search to see if someone has applied the projected gradient method to a similar non-convex problem and shown convergence. If so you'll want to cite that work as well.

wonko
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  • Thanks for your help. I found references about projected gradient but all of them are different from this method. The main benefit of this method is to reduce the line search for the step size from (0 to infinity) to (0 to 2*pi). Actually, I didn't find any reference talk about this method although it has less time overhead. – Unknown Jul 23 '14 at 04:32