Efficient Generalized Conditional Gradient with Gradient Sliding for Composite Optimization

For particular sparse optimization problems, among them is the popular tasks, its low computation cost of linear subproblem proximal gradient (PG) based approach ([Beck and Teboulle, evaluation on each iteration leads to superior 2009]; [Nesterov, 2013]). This kind of methods can achieve practical performance. However, the inferior iteration the optimal rate of convergence under certain problem settings, complexity incurs excess number of gradient hence it enjoys low iteration complexity. The periteration evaluations, which can counteract the efficiency cost mainly comes from gradient evaluation and a gained by solving low cost linear subproblem. In proximal map (PM) related to the type of the regularizer. On this paper, we therefore propose a novel algorithm the one hand, due to the optimal iteration complexity, the that requires optimal graduate evaluations as proximal number of gradient evaluations is optimal for PG method.