scholarly journals Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems

2021 ◽  
Author(s):  
Zheng Zhou ◽  
Bing Tan ◽  
Songxiao Li
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Variational Inclusion ◽  
Iterative Sequence ◽  
Inclusion Problem ◽  
Step Size ◽  
Hybrid Steepest Descent Method ◽  
Variational Inclusion Problem ◽  
Size Criterion

In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. As well as, the iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.

scholarly journals The Hybrid Steepest Descent Method for Split Variational Inclusion and Constrained Convex Minimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jitsupa Deepho ◽  
Poom Kumam
Keyword(s):  
Descent Method ◽  
Convex Minimization ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Constrained Convex Minimization ◽  
Hybrid Steepest Descent Method ◽  
Variational Inclusion Problem

We introduced an implicit and an explicit iteration method based on the hybrid steepest descent method for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem.

scholarly journals Hybrid Steepest Descent Viscosity Method for Triple Hierarchical Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
L.-C. Ceng ◽  
Q. H. Ansari ◽  
C.-F. Wen
Keyword(s):  
Approximate Solution ◽  
Variational Inequality Problem ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Viscosity Method ◽  
Hybrid Steepest Descent Method ◽  
Triple Hierarchical Variational Inequalities ◽  
Triple Hierarchical Variational Inequality ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (in short, THVIP). By combining hybrid steepest descent method, viscosity method, and projection method, we propose an approximation method to compute the approximate solution of THVIP. We also study the strong convergence of the sequences generated by the proposed method to a solution of THVIP.

Self-Interference Cancellation in Full Duplex Communication using Steepest Descent Method

2021 ◽  
Vol 9 (VI) ◽  
pp. 1433-1442
Author(s):  
N. Alivelu Manga
Keyword(s):  
Interference Cancellation ◽  
Descent Method ◽  
Steepest Descent ◽  
Full Duplex ◽  
Steepest Descent Method ◽  
Interference Signal ◽  
Least Mean Square ◽  
Echo Canceller ◽  
Step Size ◽  
Signal Processing Technique

The present-day communication system uses Frequency Division Duplex (FDD) to emulate the benefits of Full Duplex Communication. But it requires more bandwidth as the cost of the spectrum is very high it becomes a major limitation. To overcome this problem implementation of Full Duplex Communication is the best solution. Implementation of full duplex communication is difficult because of a significant problem called self-interference. while transmitting and receiving signals on the same frequency band, receiving signal is interfered with the transmitted signal this phenomenon is called self-interference. The objective of this project is to minimize that self-interference signal from the received signal by using signal processing technique, LMS echo cancellation. Least Mean Square (LMS) echo canceller whose coefficients are updated iteratively is used to cancel the self-interference. An algorithm based on steepest descent method is used to obtain coefficients that change iteratively with varying step size to solve Weiner-Hopfs equation.

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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