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OPTIMAL APPROXIMATE SOLUTION OF THE MATRIX EQUATION AXB=C OVER SYMMETRIC MATRICES 认领 引用 被引量：3
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作者 Anping Liao Yuan Lei 《Journal of Computational Mathematics》 SCIE EI 2007年第5期543-552,共10页
Let SE denote the least-squares symmetric solution set of the matrix equation A×B=C,where A,B and C are given matrices of suitable size.To find the optimal approximate solution in the set SE to a given matrix,we ... Let SE denote the least-squares symmetric solution set of the matrix equation A×B=C,where A,B and C are given matrices of suitable size.To find the optimal approximate solution in the set SE to a given matrix,we give a new feasible method based on the projection theorem,the generalized SVD and the canonical correction decomposition. 展开更多
关键词 Least-squares solution Optimal approximate solution Generalized singular value decomposition Canonical correlation decomposition.
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Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations 认领 引用
2
作者 Chunmei Li Xuefeng Duan Zhuling Jiang 《Advances in Linear Algebra & Matrix Theory》 2016年第1期1-10,共10页
Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alter... Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X0 = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective. 展开更多
关键词 Matrix Equation Dykstra’s Alternating Projection Algorithm Optimal Approximate Solution Least Norm Solution
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On Smoothing l1Exact Penalty Function for Nonlinear Constrained Optimization Problems 认领 引用 被引量：1
3
作者 Yu-Fei Ren You-Lin Shang 《Journal of the Operations Research Society of China》 EI CSCD 2026年第2期700-718,共19页
The penalty function method is a significant method for solving nonlinear constrained optimization problems(COP).In this paper,a new quadratic continuous differentiable smooth penalty function is proposed for the l_(1... The penalty function method is a significant method for solving nonlinear constrained optimization problems(COP).In this paper,a new quadratic continuous differentiable smooth penalty function is proposed for the l1exact penalty function.The error estimations between the objective function values of the smooth penalty problem,the penalty problem and the original problem are also studied.Furthermore,based on the smoothed penalty function,an algorithm for solving COP is proposed,and the convergence of the algorithm is proved.Finally,several numerical examples are given to illustrate the effectiveness of the proposed algorithm. 展开更多
关键词 l1exact penalty function Constrained optimization problem Smoothing method Approximate optimal solution
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