How to improve computing speed of mincx

Hi, I would like to ask you how to improve computing speed of mincx in linear matrix inequality.

As the number of variables increases, it takes longer to solve the linear matrix inequalities with mincx.

So, how can I improve the computing speed?

Or, do you have any ideas on how to use GPU for computing the solution of linear matrix inequality?

Answer 1

[Angelo Yeo]

Would you switch to QR as referred in the "Tip for Speed-up" in mincx?

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In LMI optimization, the computational overhead per iteration mostly comes from solving a least-squares problem of the form

where x is the vector of decision variables. Two methods are used to solve this problem: Cholesky factorization of (default), and QR factorization of A when the normal equation becomes ill conditioned (when close to the solution typically). The message

* switching to QR

is displayed when the solver has to switch to the QR mode.

Since QR factorization is incrementally more expensive in most problems, it is sometimes desirable to prevent switching to QR. This is done by setting options(4) = 1. While not guaranteed to produce the optimal value, this generally achieves a good trade-off between speed and accuracy.

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