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No tools for Convex Optimization in Mathematica??

Raffaele Santagati
Posted 10 years ago

Hello everybody,

I am trying to solve some problems that can be mapped in convex optimisation problem.

In Matlab there are some tools to help you do this, like SeDuMi or CVX

http://sedumi.ie.lehigh.edu http://cvxr.com/cvx/

But I could not find anything similar in Mathematica, on the web or in the forums.

Does anybody know if there is an easy way of implementing this kind of algorithm in Mathematica? I would like to avoid to be forced to switch to Matlab to solve this problem.

Thank you very much.
POSTED BY: Raffaele Santagati
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Thank you both very much for your answer. I was already aware of Matlink but I was thinking of finding a way of doing it from mathematica without calling external programs. I like the idea of trying to use FindMinimum. If I can find a way of making it work I will share my result, I think it could be something handy for lots of people.

Cheers
POSTED BY: Raffaele Santagati

FindMinimum can handle vector variables only for unconstrained problems, unlike CVX which can take vector and array variables.
POSTED BY: Frank Kampas

One possibility is to reformulate as an explicit optimization with constraints on variables (that is, not in terms of matrix inequalities). The link below covers the basics of how this could be done (maybe it's well known to you already). Then you can just call FindMinimum giving the objective and constraints in a list.

http://en.wikipedia.org/wiki/Semidefinite_programming

Also there may be some useful ideas at the various links below.

http://forums.wolfram.com/mathgroup/archive/2010/Dec/msg00540.html

http://stackoverflow.com/questions/5151178/quadratic-programming-in-mathematica

http://mathematica-bits.blogspot.com/2011/03/semidefinite-programming-in-mathematica.html
POSTED BY: Daniel Lichtblau

MATLAB tools, including CVX, can be called from Mathematica using MATLINK, which has been discussed on the Forum. If you do a search on MATLINK in the forum, you'll find the discussion.
POSTED BY: Frank Kampas
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