Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 25, Issue 2, Pages 214-230Publisher
INFORMS
DOI: 10.1287/moor.25.2.214.12222
Keywords
proximal point method; Bregman function; maximal monotone operator; variational inequality
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We present a new Bregman-function-based algorithm which is a modification of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. The principal advantage of the presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we eliminate the assumption of pseudomonotonicity which was, until now, standard in proving convergence for paramonotone operators. Thus we obtain a convergence result which is new even for exact generalized proximal point methods. Finally, we present some new results on the theory of Bregman functions. For example, we show that the standard assumption of convergence consistency is a consequence of the other properties of Bregman functions, and is therefore superfluous.
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