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BBN-Q / SchattenNorms.jl

Julia package providing Schatten norms, including completely bounded norms, such as Kitaev's diamond norm (ubiquitous in, e.g., quantum information processing)
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dnorm.jl could have a simplier objective function #3

Closed aoboturov closed 7 years ago

aoboturov commented 8 years ago

It looks like that instead of:

prob = maximize( retrϕ( ϕ(Jr,Ji)'*ϕ(Xr,Xi) ) )

you could just write:

prob = maximize( trace( Jr*Xr ) )

why? check eqn 1 from Approximation algorithms for Max-3-Cut and other problems via complex semidefinite programming which could also be applied here.

marcusps commented 8 years ago

Thanks for the reference! I have been looking for a good reference on the equivalence of complex and real semidefinite programs (for various other reasons). I'll check it out and make the appropriate changes.

aoboturov commented 8 years ago

I actually thought to work on that problem in relation to Convex.jl project. I am interested to contribute to the solver interface. Could I contact you somehow by email? On May 13, 2016 5:37 PM, "Marcus P S" notifications@github.com wrote:

Thanks for the reference! I have been looking for a good reference on the equivalence of complex and real semidefinite programs (for various other reasons). I'll check it out and make the appropriate changes.

— You are receiving this because you authored the thread. Reply to this email directly or view it on GitHub https://github.com/BBN-Q/SchattenNorms.jl/issues/3#issuecomment-219079424

aoboturov commented 8 years ago

proposal.pdf

I thought to do some work on it. Here's my proposal attached as a pdf.

marcusps commented 8 years ago

You can e-mail me here

aoboturov commented 8 years ago

Actually, I got the formula wrong initially. the correct one looks like:

prob = maximize( trace( Jr*Xr + Ji*Xi ) )

Fixed in #4