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I'm trying to decide whether or not a certain CS problem can be solved in polynomial time. I've got it reduced down to a basic convex optimization problem, but I can't for the life of me find a good resource that tells me when convex optimization problems are in P.

I'd like some sort of reference that has:

  • A list of common optimization algorithms
  • The restrictions on the problem that must be satisfied in order to use each of these algorithms
  • The runtime of the algorithms, in terms of $\epsilon$ (the difference between the true optimal point and the point that was returned by the algorithm).

I don't particularly need an in-depth description of the inner workings of these algorithms. I just want to know what's out there.

Thank you!

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