Inertial relaxed CQ algorithm with an application to signal processing. (English) Zbl 1489.65075
Summary: In this paper, we introduce inertial relaxed algorithm involving the self-adaptive technique for solving the split feasibility problem in Hilbert spaces which we approximate the original convex subset by a sequence of closed balls instead of half spaces. Then, the convergence results are established under mild conditions. Finally, we applied our algorithm in signal processing.
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 65K05 | Numerical mathematical programming methods |
| 47N70 | Applications of operator theory in systems, signals, circuits, and control theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
relaxed CQ algorithm; inertial algorithm; split feasibility problem; self-adaptive techniqueReferences:
| [1] | Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in product space, Numer. Algor. 8 (1994), 221-239. · Zbl 0828.65065 |
| [2] | C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl. 18 (2002) 441-453. · Zbl 0996.65048 |
| [3] | C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl. 20 (2004) 103-120. · Zbl 1051.65067 |
| [4] | Q. Yang, The relaxed CQ algorithm solving the split feasibility problem. Inverse Probl. 20 (2004 1261-1266. · Zbl 1066.65047 |
| [5] | F. Wang, H. Yu, An inertial relaxed CQ algorithm with an application to the LASSO and elastic net, Optimization (2020) https://doi.org/10.1080/02331934.2020.1763989. · Zbl 1539.47111 |
| [6] | G. L´opez, V. Mart´ın-m´arquez, F. Wang, H.K. Xu, Solving the split feasibility problem without prior knowledge of matrix norms, Inverse Probl. 28 (2012) 085004. · Zbl 1262.90193 |
| [7] | S. Kesornprom, P. Cholamjiak, On Inertial Relaxation CQ Algorithm for Split feasibility problems, Communications in Mathematics and Applications 10 (2019) 245- 255. |
| [8] | S. Kesornprom, N. Pholasa, P. Cholamjiak, On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem, Numer. Algor. 84 (2020) 997-1017. · Zbl 1459.65073 |
| [9] | G.A. Okeke, M. Abbas, M. de la Sen, Inertial subgradient extragradient Methods for solving variational inequality problems and fixed pointpProblems, Axioms 9 (2020) 51. |
| [10] | S. Suantai, N. Eiamniran, N. Pholasa, P. Cholamjiak, Three-step projective methods for solving the split feasibility problems, Mathematics 7 (2019) 712. |
| [11] | A. Padcharoen, D. Kitkuan, W. Kumam, P. Kumam, Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems, Computational and Mathematical Methods (2020) e1088. · Zbl 1432.90113 |
| [12] | A. Padcharoen, P. Kumam, Y.J. Cho, Split common fixed point problems for demicontractive operators, Numer. Algor. 82 (2019) 297-320. · Zbl 07101813 |
| [13] | S. Suantai, Y. Shehu, P. Cholamjiak, O.S. Iyiola, Strong convergence of a selfadaptive method for the split feasibility problem in Banach spaces, J. Fixed Point Theory Appl. (2018) 20:68 https://doi.org/10.1007/s11784-018-0549-y. · Zbl 1518.47107 |
| [14] | A. Padcharoen, P. Kumam, Y.J. Cho, P. Thounthong, A modified iterative algorithm for split feasibility problems of right Bregman strongly quasi-nonexpansive mappings in Banach spaces with applications, Algorithms 9 (2016) 75. · Zbl 1466.47046 |
| [15] | P. Cholamjiak, P. Sunthrayuth, A Halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces, Filomat 32 (2018) 3211-3227. · Zbl 1497.47092 |
| [16] | D. Kitkuan, P. Kumam, V. Berinde, A Padcharoen, Adaptive algorithm for solving the SCFPP of demicontractive operators without a priori knowledge of operator norms, Analele Universitatii“ Ovidius” Constanta-Seria Matematica, 27 (2019) 153- 175. · Zbl 1482.47136 |
| [17] | S. Suantai, N. Pholasa, P. Cholamjiak, The modified inertial relaxed CQ algorithm for solving the split feasibility problems, J. Indust. Manag. Optim. 14 (2018) 1595- 1615. |
| [18] | A. Padcharoen, P. Sukprasert, Nonlinear operators as concerns convex programming and applied to signal processing, Mathematics 7 (2019) 866. |
| [19] | N.T. Vinh, P. Cholamjiak, S. Suantai, A new CQ algorithm for solving split feasibility problems in Hilbert spaces, Bull. Malays. Math. Sci. Soc. 42 (2019) 2517-2534. · Zbl 1529.47117 |
| [20] | S. Suantai, N. Pholasa and P. Cholamjiak, Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems, RACSAM. 113 (2019) 1081-1099. · Zbl 1461.47035 |
| [21] | H.H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert spaces, Gewerbestrasse: Springer-Verlag, 2011. · Zbl 1218.47001 |
| [22] | H.K. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Probl. 26 (2010) 105018. · Zbl 1213.65085 |
| [23] | F. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
