Abstract
In this paper, a new inexact parallel splitting algorithm based on the shrinkage algorithm is proposed. We bring in inexact terms, and new iteration points are obtained by the parallel splitting method. A new descent direction and a proper step length are derived. Under reasonable assumptions, the convergence of the algorithm is demonstrated. Some matrix correction problem experiments show that the algorithm is efficient and easy to implement.
Highlights
A new inexact parallel splitting algorithm based on the shrinkage algorithm is proposed
We bring in inexact terms, and new iteration points are obtained by the parallel splitting method
There exist quite a few structured optimizations arising from the fields such as electronic engineering and computer science, including matrix processing [1], traffic network analysis [2], least squares semidefinite programming problem [3, 4], image restoration problem [5], and so on
Summary
A new inexact parallel splitting algorithm based on the shrinkage algorithm is proposed. We bring in inexact terms, and new iteration points are obtained by the parallel splitting method. Some matrix correction problem experiments show that the algorithm is efficient and easy to implement. Eckstein and Bertsekas first introduced an inexact technique used to solve the ADM algorithm in [12], which has been widely used and popularized (for details, refer to the bibliography [17,18,19,20,21,22,23,24,25,26,27,28,29,30]).
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