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Extending scope of robust optimization: comprehensive robust counterparts of uncertain problems. (English) Zbl 1134.90042

Summary: In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual robust optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set.
The extension of robust optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C05 Linear programming
90C25 Convex programming
90C34 Semi-infinite programming
93C55 Discrete-time control/observation systems
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References:

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