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“Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem
Ist Teil von
Journal of global optimization, 2018-06, Vol.71 (2), p.341-360
Ort / Verlag
New York: Springer US
Erscheinungsjahr
2018
Link zum Volltext
Quelle
SpringerLink
Beschreibungen/Notizen
In this paper, first, we review the projection and contraction methods for solving the split feasibility problem (SFP), and then by using the inverse strongly monotone property of the underlying operator of the SFP, we improve the “optimal” step length to provide the modified projection and contraction methods. Also, we consider the corresponding relaxed variants for the modified projection and contraction methods, where the two closed convex sets are both level sets of convex functions. Some convergence theorems of the proposed methods are established under suitable conditions. Finally, we give some numerical examples to illustrate that the modified projection and contraction methods have an advantage over other methods, and improve greatly the projection and contraction methods.