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| Volume 4, Number 3, September 2008, pp. 383-391 | |||||||||
| Heinz H. Bauschke and Patrick L. Combettes | |||||||||
| Key words: | |||||||||
| Dykstra's algorithm, maximal monotone operator, resolvent, proximity operator, von Neumann's algorithm | |||||||||
| Mathematices Subject Classification: 47H05; 47J25, 49M29, 65K05, 90C25 | |||||||||
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| Abstract: | |||
| Dykstra's algorithm employs the projectors onto two closed convex sets in a Hilbert space to construct iteratively the projector onto their intersection. In this paper, we use a duality argument to devise an extension of this algorithm for constructing the resolvent of the sum of two maximal monotone operators from the individual resolvents. This result is sharpened to obtain the construction of the proximity operator of the sum of two proper lower semicontinuous convex functions. | |||
| A Dykstra-like algorithm for two monotone operators | ||