# LMI (Linear Matrix Inequalities)

Hello.

I installed SAGE and I was very happy with the results it gave in the very beginning.

However, the reason I installed it was because I need an open-source alternative for solving Linear matrix inequalities (LMIs). I did not find an LMI solver in SAGE, though.

I will be very delighted if you help me with this issue.

Yours faithfully,

Slavi Slavchev, PA (Professor Assistant) Sofia University 'St Kliment Ohridski', Bulgaria

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Can you give a short example of what an LMI is and what the solution would be?

( 2010-11-09 16:47:47 -0500 )edit

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I think this is an OR/LP/optimization concept you want, right? Sage includes interfaces to several such programs, including CPLEX (though I don't know how comprehensive it is), and has cvxopt as a standard package. See for instance the cvxopt documentation for more details about convex optimization, which says the following:

The linear inequality is a generalized inequality with respect to a proper convex cone. It may include componentwise vector inequalities, second-order cone inequalities, and linear matrix inequalities.

Scipy is also included, and may have some of what you are looking for, as may GLPK, which may not yet be standard (I can't recall, though it's been discussed recently). In addition, we'd welcome additional help integrating the resources these programs bring to Sage, if you find you are interested in this!

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To me, your Linear Matrix Inequalities really sound like Linear Programming... And if it actually is linear programming, you may be glad to learn that GLPK, Coin, and CPLEX can be used through Sage to solve LP (GLPK being installed as a standard package).

Here is an introduction to LP using Sage

Here is the documentation page for the MixedIntegerLinearProgram class (your second best friend when dealing with LP)

Nathann

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It might be too late but you here is CVXOPT, the solver for convex optimization: http://www.sagemath.org/doc/numerical...

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Actually, this is what I want to do:

I checked the materials you supplied, but I'm afraid they won't help much. Any other ideas?

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