Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems

摘要

In this paper we study nonconvex and nonsmooth optimization problems withsemi-algebraic data, where the variables vector is split into several blocks ofvariables. The problem consists of one smooth function of the entire variablesvector and the sum of nonsmooth functions for each block separately. We analyzean inertial version of the Proximal Alternating Linearized Minimization (PALM)algorithm and prove its global convergence to a critical point of the objectivefunction at hand. We illustrate our theoretical findings by presentingnumerical experiments on blind image deconvolution, on sparse non-negativematrix factorization and on dictionary learning, which demonstrate theviability and effectiveness of the proposed method.