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