Inertial proximal alternating minimization for nonconvex and nonsmooth problems - Zhang, Yaxuan; He, Songnian (Journal of inequalities and applications, 2017)
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 .