Convergence analysis of an ALF-based nonconvex splitting algorithm with SQP structure

Abstract

<p style='text-indent:20px;'>In this paper, by combining the splitting method of augmented Lagrange function (ALF) with the sequential quadratic programming (SQP) approximation, a novel ALF-based splitting algorithm with SQP structure is proposed for multi-block linear constrained nonconvex separable optimization. The new algorithm uses ALF-based splitting idea to decompose the original problem into several small-scale subproblems. Meanwhile, the SQP approximation and Armijo-type line search are used to solve some subproblems with smoothness concurrently. Under the conventional weak hypothesis, the decreasing property of ALF as merit function is obtained. Furthermore, the global convergence, strong convergence and convergence rate results of the new algorithm in general sense are given.</p>