A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems

Abstract In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by sum possibly and differentiable with Lipschitz continuous gradient, subtracted weakly convex function. This general framework allows us to tackle problems involving loss functions specific constraints, it has many applications such as signal recovery, compressed sensing, optimal power flow distribution. We develop proximal subgradient algorithm extrapolation for solving these guaranteed subsequential convergence stationary point. The whole sequence generated our also established under widely used Kurdyka–Łojasiewicz property. To illustrate promising numerical performance proposed algorithm, conduct experiments on two important models. These include sensing problem regularization an distributed energy resources.