Inertial proximal gradient method using adaptive stepsize for convex minimization problems. (English) Zbl 07829174
Summary: This work aims to propose an inertial proximal gradient method using the adaptive stepsize to solve unconstrained minimization problems. We prove that our algorithm weakly converges to a solution of the problems. Finally, we give numerical experiments on image restoration problem. It shows that the proposed algorithms outrun known algorithms introduced by many authors.
MSC:
| 65K05 | Numerical mathematical programming methods |
| 90C25 | Convex programming |
| 90C30 | Nonlinear programming |
References:
| [1] | J.Y.B. Cruz, T.T. Nghia, On the convergence of the forward-backward splitting method with linesearches, Optimization Methods and Software 31 (6) (2016) 1209-1238. · Zbl 1354.65116 |
| [2] | K. Kankam, N. Pholasa, P. Cholamjiak, On convergence and complexity of the mod-ified forwardbackward method involving new linesearches for convex minimization, Mathematical Methods in the Applied Sciences 42 (5) (2019) 1352-1362. · Zbl 1461.65162 |
| [3] | K. Kankam, P. Cholamjiak, Strong convergence of the forward-backward splitting algorithms via linesearches in Hilbert spaces, Applicable Analysis (2021) 1-20. |
| [4] | K. Kankam, N. Pholasa, P. Cholamjiak, Hybrid forward-backward algorithms using linesearch rule for minimization problem, Thai Journal of Mathematics (2019) 17 (3) 607-625. · Zbl 07447682 |
| [5] | S. Suantai, K. Kankam, P. Cholamjiak, A novel forward-backward algorithm for solving convex minimization problem in Hilbert spaces, Mathematics (2020) 8 (1) 42. |
| [6] | P. Cholamjiak, S. Suantai, Convergence analysis for a system of equilibrium problems and a countable family of relatively quasi-nonexpansive mappings in Banach spaces, Abstract and Applied Analysis 2010 (2010). · Zbl 1206.47069 |
| [7] | S. Suantai, W. Cholamjiak, P. Cholamjiak, An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces, Applied Mathematics Letters 25 (11) (2012) 1656-1660. · Zbl 1509.47105 |
| [8] | P. Cholamjiak, S. Suantai, A new CQ algorithm for solving split feasibility problems in Hilbert spaces, Bulletin of the Malaysian Mathematical Sciences Society 42 (5) (2019) 2517-2534. · Zbl 1529.47117 |
| [9] | A. Moudafi, M. Oliny, Convergence of a splitting inertial proximal method for mono-tone operators, Journal of Computational and Applied Mathematics 155 (2) (2003) 447-454. · Zbl 1027.65077 |
| [10] | A. Beck, M.A. Teboulle, Fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences 2 (1) (2009) 183-202. · Zbl 1175.94009 |
| [11] | M. Verma, K.K. Shukla, A new accelerated proximal gradient technique for regular-ized multitask learning framework, Pattern Recognition Letters 95 (2017) 98-103. |
| [12] | A. Hanjing, S. Suantai, A fast image restoration algorithm based on a fixed point and optimization method, Mathematics 8 (3) (2020) 378. |
| [13] | D.V. Hieu, P.K. Anh, Modified forward-backward splitting method for variational inclusions, 4OR 19 (1) (2021) 127-151. · Zbl 1472.65065 |
| [14] | K.K. Tan, H.K. Xu, Approximating fixed points of non-expansive mappings by the Ishikawa iteration process, Journal of Mathematical Analysis and Applications 178 (1993) 301-301. · Zbl 0895.47048 |
| [15] | R.P. Agarwal, D.O. Regan, D.R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Topological Fixed Point Theory and Its Applications, Springer, New York -USA, 2009. · Zbl 1176.47037 |
| [16] | H.H. Bauschke, P.L. Combettes,Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, 2011. · Zbl 1218.47001 |
| [17] | Z. Opial, Weak convergence of the sequence of successive approximations for non-expansive mappings, Bulletin of the American Mathematical Society 73 (4) (1967) 591-597. · Zbl 0179.19902 |
| [18] | A.N. Iusem, B.F. Svaiter, M. Teboulle, Entropy-like proximal methods in convex programming, Mathematics of Operations Research 19 (4) (1994) 790-814. · Zbl 0821.90092 |
| [19] | Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: from error visibility to structural similarity, IEEE Transactions on Image Processing 13 (4) (2004) 600-612. |
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.
