A Generalization of the Proximal Point Algorithm
Cu Duong Ha · SIAM Journal on Control and Optimization · 1990
The problem considered in this paper is to find a solution to the generalized equation $0 \in T(x,y)$, where T is a maximal monotone operator on the product $H_1 \times H_2 $ of two Hilbert spaces $H_1 $ and $H_2 $. We give a generalization of the proximal map and the proximal point algorithm in which the proposed iterative procedure is based on just one variable. Applying to convex programming problems, instead of adding a quadratic term for all variables as in the proximal point algorithm, a quadratic term for a subset of variables is added. This paper proves that under a mild assumption our algorithm has the same convergence properties as the regular proximal point algorithm.