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A direct search method instead of a coordinate descent iterative LMI algorithm

version 1.3.0.0 (12.3 KB) by Emile Simon
Illustrates on an example the efficiency of using a direct search method (instead of an ILMI).

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Updated 25 Mar 2012

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The point of this work is given in the short paper "Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms" http://arxiv.org/abs/1110.2615

In short, the point is to illustrate that instead of developing or using what can be described as coordinate-descent iterative LMI algorithms, which are not guaranteed to converge even to locally optimal solutions, there exist many methods with better convergence properties (in theory and/or in practice).
This should be of interest for a sizeable part of the systems and control community, considering the large number of research still being made on developping this kind of algorithms which are not supported by a (strong) convergence analysis.
Note that there exist some few iterative LMI algorithms that have such proof of convergence, and these do not rely (at all or only) on a coordinate descent principle, see for instance http://www.kuleuven.be/optec/software/BMIsolver (copy on http://arxiv.org/abs/1109.3320).

The problem considered is the same as in "Hinf Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach": http://dx.doi.org/10.1109/TAC.2010.2053471
The issue with the technique proposed in that paper is that it is not guaranteed to converge even to locally optimal solutions.
In theory, there are optimization methods with better convergence properties that would therefore be more adequate.
In practice, there are many optimization methods quickly available and easy to use which will lead to solutions with better performance levels.

For more explanations and experiment results, see http://arxiv.org/abs/1104.5183
For the main points of this study, see the to-the-point paper http://arxiv.org/abs/1110.2615

Cite As

Emile Simon (2020). A direct search method instead of a coordinate descent iterative LMI algorithm (https://www.mathworks.com/matlabcentral/fileexchange/33219-a-direct-search-method-instead-of-a-coordinate-descent-iterative-lmi-algorithm), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (3)

Emile Simon

For more details about restarting Nelder-Mead (e.g. fminsearch) to improve its convergence, see the description and file on http://www.mathworks.com/matlabcentral/fileexchange/33328

Emile Simon

Second version available, heavily commented.
See the short preprint on http://arxiv.org/abs/1110.2615 for important points.

See the different preprint on http://arxiv.org/abs/1104.5183 for some other experiment results.

Emile Simon

The first version of this program has a small implementation problem. The second version will be available shortly, with more comments.

MATLAB Release Compatibility
Created with R2007b
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