In this paper, we propose and analyze an accelerated augmented Lagrangian method（denoted by AALM） for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O（1/k^2） whil...In this paper, we propose and analyze an accelerated augmented Lagrangian method（denoted by AALM） for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O（1/k^2） while the convergence rate of the classical augmented Lagrangian method（ALM） is O1 k. Numerical experiments on the linearly constrained 1-2minimization problem are presented to demonstrate the effectiveness of AALM.展开更多
Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and r...Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.展开更多
In this paper, we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation AXB ＋ CXTD = E arising in the control theory, where A, B, C, D and E ar...In this paper, we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation AXB ＋ CXTD = E arising in the control theory, where A, B, C, D and E are given matrices of suitable sizes. If the matrix equation is consistent （inconsistent）, then the solution （the least squares solution） can be obtained. Preliminary convergence properties of the proposed algorithms are presented. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and CPU time than some existing algorithms on the tested problems.展开更多
基金Supported by Fujian Natural Science Foundation(2016J01005)Strategic Priority Research Program of the Chinese Academy of Sciences(XDB18010202)
文摘In this paper, we propose and analyze an accelerated augmented Lagrangian method（denoted by AALM） for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O（1/k^2） while the convergence rate of the classical augmented Lagrangian method（ALM） is O1 k. Numerical experiments on the linearly constrained 1-2minimization problem are presented to demonstrate the effectiveness of AALM.
文摘Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.
文摘In this paper, we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation AXB ＋ CXTD = E arising in the control theory, where A, B, C, D and E are given matrices of suitable sizes. If the matrix equation is consistent （inconsistent）, then the solution （the least squares solution） can be obtained. Preliminary convergence properties of the proposed algorithms are presented. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and CPU time than some existing algorithms on the tested problems.
