Inertial proximal alternating minimization for nonconvex and nonsmooth problems

In this paper, we study the minimization problem of the type L(x, y) = f(x) + R(x, y) + g(y), where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function H that guarantees a sufficient decrease property of the iterates. In fact, we prove that if H satisfies the Kurdyka-Lojasiewicz inequality, then every bounded sequence generated by the algorithm converges strongly to a critical point of L.