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Given the wide range of optimization methods, which is the appropriate method to use? I am thinking of using either linear programming (interior-point methods) or augmented Lagrangian methods. Which method will be more approriate for large scale linear problem with equality constraint? Thank you.

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I am thinking more from the perspective of the method's strengths. I am more inclined to use augmented Lagrangian method than linear programming, as it is easier to understand. Is there any other strengths of the augmented Lagrangian method over linear programming? – Michael Mar 12 '12 at 16:19

I would recommend you to grab a copy of matlab as many linear programming algorithms are implemented and you can directly compare how they perform on your data.

However it should also be a good hint to see what they use for your problem:

The default large-scale method is based on LIPSOL ([52]), which is a variant of Mehrotra's predictor-corrector algorithm ([47]), a primal-dual interior-point method.

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