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HsiaoHan Chao(suzichaoucla.edu) Abstract: Signal processing applications of semidefinite optimization are often rooted in sumofsquares representations of nonnegative trigonometric polynomials. Interiorpoint solvers for semidefinite optimization can handle constraints of this form with a periterationcomplexity that is cubic in the degree of the trigonometric polynomial. The purpose of this paper is to discuss firstorder methods with a lower complexity per iteration. The methods are based on generalized proximal operators defined in terms of the ItakuraSaito distance. This is the Bregman distance defined by the negative entropy function. The choice for the ItakuraSaito distance is motivated by the fact that the associated generalized projection on the set of normalized nonnegative trigonometric polynomials can be computed at a cost that is roughly quadratic in the degree of the polynomial. The generalized projection is the key operation in generalized proximal firstorder methods that use Bregman distances instead of the squared Euclidean distance. The paper includes numerical results with Auslender and Teboulle's accelerated proximal gradient method for Bregman distances. Keywords: Category 1: Convex and Nonsmooth Optimization Category 2: Linear, Cone and Semidefinite Programming Citation: Download: [PDF] Entry Submitted: 03/29/2018 Modify/Update this entry  
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