Recent results on the analytic center approach for bounded error parameter estimation
In this paper, we present an overview of some recent work  on the so-called analytic center approach for bounded error parameter estimation. First, we discuss the optimality properties of well-known algorithms such as the Chebychev center, the projection and the min-max estimates. Subsequently, we propose the analytic center as an alternative algorithm for recursive estimation. We show that the analytic center minimizes the output error and, on the contrary of other estimates like Chebychev, allows for an easy-to-compute sequential algorithm. We argue that the maximum number of Newton iterations required to evaluate a sequence of analytic centers is linear in the number of observed data points and it is comparable to the complexity of off-line algorithms for estimating a single analytic center. Finally, we briefly discuss a number of open problems which are currently under investigation.
KeywordsLinear Matrix Inequality Analytic Center Interior Point Method Newton Iteration Output Error
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