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 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.

scholarly journals General Split Feasibility Problems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Eslamian ◽  
Abdul Latif
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility

Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

scholarly journals The Combination Projection Method for Solving Convex Feasibility Problems

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 249 ◽  
Author(s):  
Songnian He ◽  
Qiao-Li Dong
Keyword(s):  
Hilbert Space ◽  
Positive Integer ◽  
Weak Convergence ◽  
Level Set ◽  
Projection Method ◽  
Real Hilbert Space ◽  
Convex Combination ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Convex Feasibility

In this paper, we propose a new method, which is called the combination projection method (CPM), for solving the convex feasibility problem (CFP) of finding some x * ∈ C : = ∩ i = 1 m { x ∈ H | c i ( x ) ≤ 0 } , where m is a positive integer, H is a real Hilbert space, and { c i } i = 1 m are convex functions defined as H . The key of the CPM is that, for the current iterate x k , the CPM firstly constructs a new level set H k through a convex combination of some of { c i } i = 1 m in an appropriate way, and then updates the new iterate x k + 1 only by using the projection P H k . We also introduce the combination relaxation projection methods (CRPM) to project onto half-spaces to make CPM easily implementable. The simplicity and easy implementation are two advantages of our methods since only one projection is used in each iteration and the projections are also easy to calculate. The weak convergence theorems are proved and the numerical results show the advantages of our methods.

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