Stochastic Approximation Approach for Consensus and Convergence Rate Analysis of Multiagent Systems

2012 ◽  
Vol 57 (12) ◽  
pp. 3163-3168 ◽  
Author(s):  
Juanjuan Xu ◽  
Huanshui Zhang ◽  
Lihua Xie
Keyword(s):  
Convergence Rate ◽  
Multiagent Systems ◽  
Stochastic Approximation ◽  
Approximation Approach ◽  
Rate Analysis ◽  
Convergence Rate Analysis

scholarly journals Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 608
Author(s):  
Pornsarp Pornsawad ◽  
Parada Sungcharoen ◽  
Christine Böckmann
Keyword(s):  
Convergence Rate ◽  
Potential Problem ◽  
Regularization Parameter ◽  
Discrepancy Principle ◽  
Source Condition ◽  
Rate Analysis ◽  
Potential Problems ◽  
Ill Posed ◽  
Landweber Method ◽  
Convergence Rate Analysis

In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.

A modified limited memory steepest descent method motivated by an inexact super-linear convergence rate analysis

2020 ◽  
Author(s):  
Ran Gu ◽  
Qiang Du
Keyword(s):  
Convergence Rate ◽  
Linear Convergence ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Step Size ◽  
Linear Convergence Rate ◽  
Limited Memory ◽  
Rate Analysis ◽  
Convergence Rate Analysis

Abstract How to choose the step size of gradient descent method has been a popular subject of research. In this paper we propose a modified limited memory steepest descent method (MLMSD). In each iteration we propose a selection rule to pick a unique step size from a candidate set, which is calculated by Fletcher’s limited memory steepest descent method (LMSD), instead of going through all the step sizes in a sweep, as in Fletcher’s original LMSD algorithm. MLMSD is motivated by an inexact super-linear convergence rate analysis. The R-linear convergence of MLMSD is proved for a strictly convex quadratic minimization problem. Numerical tests are presented to show that our algorithm is efficient and robust.

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