Fixed Points of Averages of Resolvents: Geometry and Algorithms
SIAM Journal on Optimization
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
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Presents parallel projection methods to find least-squares solutions to inconsistent convex set theoretic signal synthesis problems. The problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space, where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the Cartesian product of the original sets. A solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space. The convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated