On Inertial Relaxation CQ Algorithm for Split Feasibility Problems

Prasit Cholamjiak, Suparat Kesornprom


In this work, we introduce an inertial relaxation CQ algorithm for the split feasibility problem in Hilbert spaces. We prove weak convergence theorem under suitable conditions. Numerical examples illustrating our methods’s efficiency are presented for comparing some known methods.


Split feasibility problem; CQ algorithm; Hilbert space; Projection; Inertial

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Bauschke, H.H, Borwein, J. M.: On projection algorithms for solving convex feasibility problems SIAM Rev. 38, 367-426(1996)

Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, London (2011)

Bot, R. I., Csetnek, E. R., Hendrich, C.: Inertial DouglasRachford splitting for monotone inclusion problems. Applied Mathematics and Computation, 256, 472-487(2015)

Byrne, C.: Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 18, 441-453 (2002)

Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20, 103-120 (2004)

Censor, Y., Elfving, T.: A multiprojection algorithms using Bregman projection in a product space. Numer. Algor. 8, 221-239 (1994)

Dang, Y., Sun, J., Xu, H.: Inertial accelerated algorithms for solving a split feasibility problem, J. Ind. Manag. Optim. Doi: 103934/jimo.2016078

Dong, Q.L., Tang, Y.C., Cho, Y.J., Rassias, T.M.: . Optimal choice of the step length of the projection and contraction methods for solving the split feasibility problem. Journal of Global Optimization, 71(2), 341-360(2018).

Gibali, A., Liu, L.W., Tang, Y.C.: Note on the modified relaxation CQ algorithm for the split feasibility problem. Optimization Letters. 12, 1-14 (2017)

Mainge, P.E.: Convergence theorem for inertial KM-type algorithms, Journal of Computational and Applied Mathematics. 219, 223-236(2008).

Qu, B., Xiu, N.: A note on the CQ algorithm for the split feasibility problem. Inverse Prob. 21, 1655-1665 (2005)

Stark, H.: Image Recovery: Theory and Applications (San Diego, CA: Academic) Stark H Iterative algorithms for the multiple-sets split feasibility problem Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems ed Censor,Y., Jiang, M., Wang, G.: (Madison, WI: Medical Physics Publishing) 243-79(2010)

Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 58, 267-288 (1996)

Yang, Q.: The relaxed CQ algorithm for solving the split feasibility problem. Inverse Prob. 20, 1261-1266 (2004)

Zhang,W., Han, D., Li, Z.: A self-adaptive projectionmethod for solving themultiple-sets split feasibility problem. Inverse Probl. 25, 115001 (2009)

Bauschke, H.H., Combettes, P.L.: A weak-to-strong convergence principle for Fej´er-monotone methods in Hilbert spaces. Math. Oper. Res. 26, 248-264 (2001)


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