An Efficient Linearly Convergent Regularized Proximal Point Algorithm for Fused Multiple Graphical Lasso Problems

Nowadays, analysing data from different classes or over a temporal grid has attracted great deal of interest. As result, various multiple graphical models for learning collection simultaneously have been derived by introducing sparsity in graphs and similarity across graphs. This paper focuses on the fused Lasso model which encourages not only shared pattern sparsity, but also values edges For solving this model, we develop an efficient regularized proximal point algorithm, where subproblem each iteration algorithm is solved superlinearly convergent semismooth Newton method. To implement method, derive explicit expression generalized Jacobian mapping regularizer. Unlike those widely used first order methods, our approach heavily exploited underlying second information through can accelerate convergence improve its robustness. The efficiency robustness proposed are demonstrated comparing with some state-of-the-art methods both synthetic real sets. Supplementary materials article available online.