scholarly journals ANALYSIS OF THE INEXACT UZAWA ALGORITHMS FOR NONLINEAR SADDLE-POINT PROBLEMS

2010 ◽  
Vol 51 (3) ◽  
pp. 369-382 ◽  
Author(s):  
JIAN-LEI LI ◽  
TING-ZHU HUANG ◽  
LIANG LI
Keyword(s):  
Saddle Point ◽  
Numerical Experiments ◽  
Sufficient Condition ◽  
Saddle Point Problems ◽  
Simple Sufficient Condition ◽  
Inexact Uzawa Algorithms

AbstractInexact Uzawa algorithms for solving nonlinear saddle-point problems are proposed. A simple sufficient condition for the convergence of the inexact Uzawa algorithms is obtained. Numerical experiments show that the inexact Uzawa algorithms are convergent.

scholarly journals A Restless Bandit Model for Resource Allocation, Competition, and Reservation

2021 ◽  
Author(s):  
Jing Fu ◽  
Bill Moran ◽  
Peter G. Taylor
Keyword(s):  
Resource Allocation ◽  
Numerical Experiments ◽  
Asymptotic Optimality ◽  
Sufficient Condition ◽  
Limited Capacity ◽  
Index Policy ◽  
Asymptotically Optimal ◽  
Restless Bandit ◽  
Simple Sufficient Condition ◽  
Resource Capacity

In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.

A Fast Shift-Splitting Iteration Method for Nonsymmetric Saddle Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Quan-Yu Dou ◽  
Jun-Feng Yin ◽  
Ze-Yu Liao
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Splitting Technique ◽  
Splitting Iteration Method

AbstractBased on the shift-splitting technique and the idea of Hermitian and skew-Hermitian splitting, a fast shift-splitting iteration method is proposed for solving nonsingular and singular nonsymmetric saddle point problems in this paper. Convergence and semi-convergence of the proposed iteration method for nonsingular and singular cases are carefully studied, respectively. Numerical experiments are implemented to demonstrate the feasibility and effectiveness of the proposed method.

scholarly journals New Preconditioning Techniques for Saddle Point Problems Arising from the Time-Harmonic Maxwell Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Qingbing Liu
Keyword(s):  
Saddle Point ◽  
Numerical Experiments ◽  
Maxwell Equations ◽  
Saddle Point Problems ◽  
Finite Element Discretization ◽  
Preconditioning Techniques ◽  
Element Discretization ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
Saddle Point Matrices

We study two parameterized preconditioners for iteratively solving the saddle point linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations in electromagnetic problems. We establish some spectral properties of the preconditioned saddle point matrices, involving the choice of the parameter. Meanwhile, we provide some results of numerical experiments to show the effectiveness of the proposed parameterized preconditioners.

A relaxed splitting preconditioner for saddle point problems

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu ◽  
Ai-Qun Huang
Keyword(s):  
Saddle Point ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Preconditioned Matrix ◽  
Appl Math

AbstractIn this paper, we introduce a relaxed splitting preconditioner for saddle point problems. Spectral properties of the preconditioned matrix are analyzed and compared with the closely related preconditioner in recent paper [New preconditioners for saddle point problems, Appl. Math. Comput. 172 (2006), 762-771] by Pan et al. Numerical experiments are given to illustrate the efficiency of the proposed precoditioner.

scholarly journals The ULT-HSS hybrid iteration method for symmetric saddle point problems

2021 ◽  
pp. 128-128
Author(s):  
Jun-Feng Lu
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Optimal Parameter ◽  
Sufficient Conditions ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Saddle Point Problems ◽  
Necessary And Sufficient ◽  
Direction Iteration

This paper proposes a hybrid iteration method for solving symmetric saddle point problem arising in computational fluid dynamics. It is an implicit alternative direction iteration method and named as the ULT-HSS method. The convergence analysis is provided, and the necessary and sufficient conditions are given for the convergence of the method. Some practical approaches are formulated for setting the optimal parameter of the method. Numerical experiments are given to show its efficiency.

scholarly journals New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
TingZhu Huang ◽  
GuangHui Cheng ◽  
Liang Li
Keyword(s):  
Saddle Point ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Optimal Parameter ◽  
Spectral Characteristics ◽  
Saddle Point Problems

We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter in practical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners.

Sign in / Sign up

Export Citation Format

Share Document