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Optimization of Entropy, Relative Entropy, etc.
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TOPIC: Optimization of Entropy, Relative Entropy, etc.
#6811
Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 0
Hi all,

I am new to Yalmip and was wondering if anyone could recommend a solver to use for entropy (users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Entropy) maximization.

I am also interested in minimizing relative entropy (en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) and mutual information (en.wikipedia.org/wiki/Mutual_information) - has anyone ever seen these implemented in Yalmip? If not, I may try writing them myself.

These are all convex optimization problems (at least under the constraints I will be using). I have tried using CVX, but I have run into problems because their solvers (including SeDuMi) are not suited to optimization of the exponential family (log, exp, etc.) - see Appendix D.1 of web.cvxr.com/cvx/cvx_usrguide.pdf.

Thanks
jmscarlett
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#6812
Re: Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 32
Through YALMIP, you would use fmincon, snopt, ipopt
lofberg
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#6813
Re: Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 32
I think I have a draft of an overloaded KL somewhere, if not, should be easy to add.

Never heard of the mutual information, so I would have to look into that first.
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#6814
Re: Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 0
Thanks! I'll try those out.

Even a draft of KL would be very handy, as I don't feel very confident about writing these myself yet.

Mutual information might not be explicitly needed, since it is a special case of KL divergence (namely, from the joint distribution P(x,y) to its marginals P(x)P(y))
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#6815
Re: Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 32
mail me and I'll hook you up with a draft (johanl@isy.liu.se)
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#6817
Re: Optimization of Entropy, Relative Entropy, etc. 11 Months ago Karma: 32
Kullback-Leibler and cross entropy have now been added to the code repository and will thus be available in the next release.
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