A Dykstra-like algorithm for two monotone operators
Heinz H. Bauschke, Patrick L. Combettes · 2007
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 argu-ment 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.