#### A. Bnouhachem, X. Qin, An inertial proximal Peaceman-Rachford splitting method with SQP regularization for convex programming, Vol. 2020 (2020), Article ID 50, pp. 1-17

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DOI: 10.23952/jnfa.2020.50

Received October 12, 2020; Accepted November 26, 2020; Published December 17, 2020

Abstract. In this paper, based on the square quadratic proximal (SQP) method and the inertial proximal Peaceman-Rachford splitting method (PRSM), we propose an inertial PRSM with the SQP regularization for solving a separable convex minimization model with positive orthant constraints. The new algorithm can be viewed as an interior version of the inertial PRSM with the SQP regularization. Under standard assumptions, the global convergence of the proposed method is proved. We show that the proposed method can find an approximate solution of the mixed variational inequalities with an accuracy of $o(1/\sqrt{k}).$