Optimization with few violated constraints and its application in controls

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Optimization with few violated constraints is a variant of the standard optimization in which a small number of constraints may be violated. It is especially useful when some of constraints are not reliable due to modeling uncertainty and/or measurement errors. In this proposal, we show that several control problems can be solved within the framework of opti-mization with few violated constraints. One example is a convergent and numerically efficient algoritlini for robust system identification in the presence of outliers.Unlike the standard optimization, however, optimization with few violated constraints has received little attention in the literature and few results are available. After demonstrating a need for optimization with few violated constraints for controls, we present our preliminary results in the proposal which include the problem set up, preliminary analysis and a numerical algorithm for solving optimization with few violated constraints. The algorithm is proven to have a low computational complexity. Preliminary results are very promising. Then, a detailed research plan in terms of the algorithm and its application is outlined in the proposal.