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 X<sub>0</sub> = 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
In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction an...In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction and its fast convergence towards an optimal solution. Our proposed method is compared with Newton＇s method for linear program named lpnew, widely used as an optimization algorithm for classification problems.展开更多
文摘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 X<sub>0</sub> = 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.
文摘In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction and its fast convergence towards an optimal solution. Our proposed method is compared with Newton＇s method for linear program named lpnew, widely used as an optimization algorithm for classification problems.
