Convergence analysis of an improved Bregman-type Peaceman-Rachford splitting algorithm for nonconvex nonseparable linearly constrained optimization problems

This study refers to a class of nonconvex nonseparable optimization problems with linear constraints and closed convex set constraints. Firstly, the equivalent transformation of the discussed problem is carried out by introducing the indicator function and the auxiliary variable. Secondly, to solve the equivalent problem of transformation, an improved Bregman-type Peaceman-Rachford splitting method is proposed by improving the Lagrange multiplier updating technique in the traditional splitting algorithm. Under the general assumptions, the global convergence of the proposed algorithm is proven. Furthermore, if the augmented Lagrange function satisfies the Kurdyka-Lojasiewicz property, the strong convergence of the proposed algorithm is established. Finally, some preliminary numerical results are shown to indicate the effectiveness of the proposed algorithm. (c) 2023 Elsevier B.V. All rights reserved.