In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) $L(x,y)=f(x)+R(x,y)+g(y)$ , 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.
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