Inertial proximal alternating minimization for nonconvex and nonsmooth problems

Abstract

In this paper, we study the minimization problem of the type , 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.

Two-step inertial Bregman alternating minimization algorithm for nonconvex and nonsmooth problems

“…Feng et al [19] focused on a minimization optimization model that is nonconvex and nonsmooth and established an inertial Douglas-Rachford splitting (IDRS) algorithm, which incorporate the inertial technique into the framework of the Douglas-Rachford splitting algorithm. Specially, for solving problem (1.1), Zhang and He [20] introduced an inertial version of the proximal alternating minimization method, Pock and Sabach [21] proposed the following inertial proximal alternating linearized minimization (iPALM) algorithm:…”