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On the road between robust optimization and the scenario approach for chance constrained optimization problems

Author(s):

K. Margellos, P.J. Goulart, J. Lygeros
Conference/Journal:

IEEE Transactions on Automatic Control, to appear
Abstract:

We propose a new method for solving chance constrained optimization problems which lies between robust (or worst-case) optimization and scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in standard robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the scenario approach. Specifically, we provide two alternatives to the standard scenario approach and show that for a given performance level, the number of scenarios is not proportional to the number of decision variables, but is proportional to the dimension of the uncertainty vector or the number of constraints respectively. Our results lead immediately to guidelines under which each of the three methods (the scenario approach and the two proposed methods) is preferable. The proposed solution methods are compared with the scenario approach by means of numerical examples.

Year:

2014
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { MarGou:2014:IFA_4259,
    author={K. Margellos and P.J. Goulart and J. Lygeros},
    title={{On the road between robust optimization and the scenario
	  approach for chance constrained optimization problems}},
    journal={IEEE Transactions on Automatic Control},
    year={2014},
    volume={},
    number={},
    pages={},
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=4259}
}
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