Selective linearization for multi-block statistical learning

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We consider the problem of minimizing a sum of several convex non-smooth functions and discuss the selective linearization method (SLIN), which iteratively linearizes all but one of the functions and employs simple proximal steps. The algorithm is a form of multiple operator splitting in which the order of processing partial functions is not fixed, but rather determined in the course of calculations. SLIN is globally convergent for an arbitrary number of component functions without artificial duplication of variables. We report results from extensive numerical experiments in two statistical learning settings such as large-scale overlapping group Lasso and doubly regularized support vector machine. In each setting, we introduce novel and efficient solutions for solving sub-problems. The numerical results demonstrate the efficacy and accuracy of SLIN.