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Brien Alkire (brienalkires.com) Abstract: We consider convex optimization problems with the constraint that the variables form a finite autocorrelation sequence, or equivalently, that the corresponding power spectral density is nonnegative. This constraint is often approximated by sampling the power spectral density, which results in a set of linear inequalities. It can also be cast as a linear matrix inequality via the positivereal lemma. The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interiorpoint methods for semidefinite programming. However, these methods require O(n^6) floating point operations per iteration, if a generalpurpose implementation is used. We introduce a much more efficient method with a complexity of O(n^3) flops per iteration. Keywords: optimization, convex, signal processing, autocorrelation Category 1: Applications  Science and Engineering (Other ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: To appear in the Proceedings of the 34th IEEE Asilomar Conference on Signals, Systems and Computer, Pacific Grove, California, October 29 through November 1, 2000. Download: Entry Submitted: 01/28/2001 Modify/Update this entry  
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