Self-adaptive projection methods for the multiple-sets split feasibility problem

2011 ◽  
Vol 27 (3) ◽  
pp. 035009 ◽  
Author(s):  
Jinling Zhao ◽  
Qingzhi Yang
Keyword(s):  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility ◽  
Self Adaptive

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

scholarly journals On Two Projection Algorithms for the Multiple-Sets Split Feasibility Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qiao-Li Dong ◽  
Songnian He
Keyword(s):  
Adaptive Algorithm ◽  
Split Feasibility Problem ◽  
Rates Of Convergence ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Numerical Tests ◽  
Split Feasibility ◽  
Self Adaptive

We present a projection algorithm which modifies the method proposed by Censor and Elfving (1994) and also introduce a self-adaptive algorithm for the multiple-sets split feasibility problem (MSFP). The global rates of convergence are firstly investigated and the sequences generated by two algorithms are proved to converge to a solution of the MSFP. The efficiency of the proposed algorithms is illustrated by some numerical tests.

scholarly journals An Inertial Accelerated Algorithm for Solving Split Feasibility Problem with Multiple Output Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Huijuan Jia ◽  
Shufen Liu ◽  
Yazheng Dang
Keyword(s):  
Strong Convergence ◽  
Numerical Experiments ◽  
Convex Sets ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Matrix Inverse ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility ◽  
Self Adaptive

The paper proposes an inertial accelerated algorithm for solving split feasibility problem with multiple output sets. To improve the feasibility, the algorithm involves computing of projections onto relaxed sets (half spaces) instead of computing onto the closed convex sets, and it does not require calculating matrix inverse. To accelerate the convergence, the algorithm adopts self-adaptive rules and incorporates inertial technique. The strong convergence is shown under some suitable conditions. In addition, some newly derived results are presented for solving the split feasibility problem and split feasibility problem with multiple output sets. Finally, numerical experiments illustrate that the algorithm converges more quickly than some existing algorithms. Our results extend and improve some methods in the literature.

scholarly journals Modified Halfspace-Relaxation Projection Methods for Solving the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Min Li
Keyword(s):  
Lower Bounds ◽  
Split Feasibility Problem ◽  
Step Length ◽  
Projection Methods ◽  
Numerical Results ◽  
Feasibility Problem ◽  
New Methods ◽  
Hrp Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility

This paper presents modified halfspace-relaxation projection (HRP) methods for solving the split feasibility problem (SFP). Incorporating with the techniques of identifying the optimal step length with positive lower bounds, the new methods improve the efficiencies of the HRP method (Qu and Xiu (2008)). Some numerical results are reported to verify the computational preference.

Sign in / Sign up

Export Citation Format

Share Document