A Dykstra-like algorithm for two monotone operators
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification: Primary 47H05; Secondary 47J25, 49M29, 65K05, 90C25.
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