A Class of Inexact Variable Metric Proximal Point Algorithms

For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are established under standard assumptions. We demonstrate the advantage of variable metric implementation in the case of solving systems of smooth monotone equations by the proximal Newton method. Key words. proximal point methods, variable metric, maximal monotone operators, approximation AMS subject classifications. 90C30, 90C33 DOI. 10.1137/070688146

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Lisandro A. Parente, Pablo A. Lotito, Mikhail V. Solodov
• Keywords: Maximal Monotone, Maximal Monotone Inclusions, Proximal Point Methods, SIAMJO 2008