scholarly journals A Novel Stochastic Stratified Average Gradient Method: Convergence Rate and Its Complexity

2018 ◽  
Author(s):  
Aixiang Andy Chen ◽  
Xiaolong Chai ◽  
Bingchuan Chen ◽  
Rui Bian ◽  
Qingliang Chen
Keyword(s):  
Convergence Rate ◽  
Gradient Method ◽  
Average Gradient

Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

2011 ◽  
Vol 1 (1) ◽  
pp. 82-88
Author(s):  
Hong-Kui Pang ◽  
Ying-Ying Zhang ◽  
Xiao-Qing Jin
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Option Pricing ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Superlinear Convergence Rate ◽  
Pricing Problems ◽  
Toeplitz Systems ◽  
Toeplitz System

AbstractWe consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

scholarly journals The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions

2021 ◽  
Author(s):  
Hadi Abbaszadehpeivasti ◽  
Etienne de Klerk ◽  
Moslem Zamani
Keyword(s):  
Convergence Rate ◽  
Gradient Method ◽  
Stationary Point ◽  
Smooth Function ◽  
Step Length ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Smooth Functions ◽  
Worst Case

AbstractIn this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an L-smooth function. We establish a new convergence rate, and show that the bound may be exact in some cases, in particular when all step lengths lie in the interval (0, 1/L]. In addition, we derive an optimal step length with respect to the new bound.

An Improved Niche Genetic Algorithm

2013 ◽  
Vol 380-384 ◽  
pp. 1444-1447
Author(s):  
Min Zhang ◽  
Xue Zhang ◽  
Yun Tao Zhang ◽  
Jin Ming
Keyword(s):  
Genetic Algorithm ◽  
Convergence Rate ◽  
Gradient Method ◽  
Research Performance ◽  
Population Diversity ◽  
Equilibrium Strategy ◽  
Migration Strategy ◽  
Local Research ◽  
Improved Algorithm

As a result of poor local research performance and short of the population diversity in niche genetic algorithm (NGA), an improved niche genetic algorithm (I-NGA) is presented in this paper. The algorithm adopts migration strategy, grading gradient method and gene equilibrium strategy, and it has better performance on accelerating the convergence rate and increasing the population diversity. This approach is used in Camel function for confirming. Through comparisons to NGA and I-NGA, the improved algorithm shows its better optimization.

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