Research Article
BibTex RIS Cite
Year 2022, , 412 - 422, 30.12.2022
https://doi.org/10.53006/rna.1143531

Abstract

References

  • Ansari, Q.H., Rehan, A. (2014). Split feasibility and fixed point problems. In: Ansari, Q.H. (ed) Nonlinear Analysis: Approximation Theory, Optimization and Applications (pp. 281-322). Birkh¨auser, Springer.
  • Bauschke, H.H., Combettes, P.L. (2011). Convex analysis and monotone operator theory in Hilbert spaces (Vol. 408). New York: Springer.
  • Beck, A., Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Science, 2(1), 183-202.
  • Bello Cruz, J.Y., Nghia, T.T. (2016). On the convergence of the forward-backward splitting method with linesearches. Optimization Methods and Software, 31(6), 1209-1238.
  • Burachik, R.S., Iusem, A.N. (2008). Enlargements of Monotone Operators. In Set-Valued Mappings and Enlargements of Monotone Operators (pp. 161-220). Springer, Boston, MA.
  • Byrne, C. (2002). Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Problems, 18(2), 441.
  • Byrne, C. (2003). A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems, 20(1), 103.
  • Ceng, L.C., Ansari, Q.H., Yao, J.C. (2012). An extragradient method for solving split feasibility and fixed point problems. Computers and Mathematics with Applications, 64(4), 633-642.
  • Censor, Y., Elfving, T. (1994). A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 8(2), 221-239.
  • Cholamjiak, W., Cholamjiak, P., Suantai, S. (2018). An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces. Journal of Fixed Point Theory and Applications, 20(1), 1-17.
  • Cholamjiak, P., Shehu, Y. (2019). Inertial forward-backward splitting method in Banach spaces with application to compressed sensing. Applications of Mathematics, 64(4), 409-435.
  • Cui, F., Tang, Y., Zhu, C. (2019). Convergence analysis of a variable metric forward–backward splitting algorithm with applications. Journal of Inequalities and Applications, 2019(1), 1-27.
  • Dang, Y., Gao, Y. (2010). The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. Inverse Problems, 27(1), 015007.
  • Ege, O., Karaca, I. (2015). Banach fixed point theorem for digital images. J. Nonlinear Sci. Appl, 8(3), 237-245.
  • Franklin, J. (1980). Methods of Mathematical Economics Springer-Verlag New York. Inc, January.
  • Hanjing, A., Suantai, S. (2020). A fast image restoration algorithm based on a fixed point and optimization method. Mathematics, 8(3), 378.
  • Hieu Van , D., Anh, P. K., Muu, L. D. (2021). Modified forward-backward splitting method for variational inclusions. 4OR, 19(1), 127-151.
  • Iusem, A.N., Svaiter, B.F., Teboulle, M. (1994). Entropy-like proximal methods in convex programming. Mathematics of Operations Research, 19(4), 790-814.
  • Lions, J. L., Stampacchia, G. (1967). Variational inequalities. Communications on pure and applied mathematics, 20(3), 493-519.
  • L´opez, G., Mart´ın-M´arquez, V., Wang, F., Xu, H.K. (2012). Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Problems, 28(8), 085004.
  • Malitsky, Y., Tam, M. K. (2020). A forward-backward splitting method for monotone inclusions without cocoercivity. SIAM Journal on Optimization, 30(2), 1451-1472.
  • Machmud, R., Wijaya, A. (2016). Behavior determinant based cervical cancer early detection with machine learning algorithm. Advanced Science Letters, 22(10), 3120-3123.
  • Osilike, M.O., Aniagbosor, S.C., Akuchu, B.G. (2002). Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, Panamerican Mathematical Journal, 12(2), 77-88.
  • Tseng, P. , A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim., 2000, 38(2), 431-446.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288.
  • Uko, L. U. (1996). Generalized equations and the generalized Newton method. Mathematical programming, 73(3), 251-268.
  • Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600-612.
  • Xu, H.K. (2010). Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Problems, 26(10), 105018.
  • Yang, Q. (2004). The relaxed CQ algorithm solving the split feasibility problem. Inverse Problems, 20(4), 1261.

A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification

Year 2022, , 412 - 422, 30.12.2022
https://doi.org/10.53006/rna.1143531

Abstract

In this paper, we propose a new proximal gradient method for a convex minimization problem in real Hilbert spaces. We suggest a new linesearch which does not require the condition of Lipschitz constant and improve conditions of inertial term which speed up performance of convergence. Moreover, we prove the weak convergence of the proposed method under some suitable conditions. The numerical implementations in data classification are reported to show its efficiency.

References

  • Ansari, Q.H., Rehan, A. (2014). Split feasibility and fixed point problems. In: Ansari, Q.H. (ed) Nonlinear Analysis: Approximation Theory, Optimization and Applications (pp. 281-322). Birkh¨auser, Springer.
  • Bauschke, H.H., Combettes, P.L. (2011). Convex analysis and monotone operator theory in Hilbert spaces (Vol. 408). New York: Springer.
  • Beck, A., Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Science, 2(1), 183-202.
  • Bello Cruz, J.Y., Nghia, T.T. (2016). On the convergence of the forward-backward splitting method with linesearches. Optimization Methods and Software, 31(6), 1209-1238.
  • Burachik, R.S., Iusem, A.N. (2008). Enlargements of Monotone Operators. In Set-Valued Mappings and Enlargements of Monotone Operators (pp. 161-220). Springer, Boston, MA.
  • Byrne, C. (2002). Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Problems, 18(2), 441.
  • Byrne, C. (2003). A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems, 20(1), 103.
  • Ceng, L.C., Ansari, Q.H., Yao, J.C. (2012). An extragradient method for solving split feasibility and fixed point problems. Computers and Mathematics with Applications, 64(4), 633-642.
  • Censor, Y., Elfving, T. (1994). A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 8(2), 221-239.
  • Cholamjiak, W., Cholamjiak, P., Suantai, S. (2018). An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces. Journal of Fixed Point Theory and Applications, 20(1), 1-17.
  • Cholamjiak, P., Shehu, Y. (2019). Inertial forward-backward splitting method in Banach spaces with application to compressed sensing. Applications of Mathematics, 64(4), 409-435.
  • Cui, F., Tang, Y., Zhu, C. (2019). Convergence analysis of a variable metric forward–backward splitting algorithm with applications. Journal of Inequalities and Applications, 2019(1), 1-27.
  • Dang, Y., Gao, Y. (2010). The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. Inverse Problems, 27(1), 015007.
  • Ege, O., Karaca, I. (2015). Banach fixed point theorem for digital images. J. Nonlinear Sci. Appl, 8(3), 237-245.
  • Franklin, J. (1980). Methods of Mathematical Economics Springer-Verlag New York. Inc, January.
  • Hanjing, A., Suantai, S. (2020). A fast image restoration algorithm based on a fixed point and optimization method. Mathematics, 8(3), 378.
  • Hieu Van , D., Anh, P. K., Muu, L. D. (2021). Modified forward-backward splitting method for variational inclusions. 4OR, 19(1), 127-151.
  • Iusem, A.N., Svaiter, B.F., Teboulle, M. (1994). Entropy-like proximal methods in convex programming. Mathematics of Operations Research, 19(4), 790-814.
  • Lions, J. L., Stampacchia, G. (1967). Variational inequalities. Communications on pure and applied mathematics, 20(3), 493-519.
  • L´opez, G., Mart´ın-M´arquez, V., Wang, F., Xu, H.K. (2012). Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Problems, 28(8), 085004.
  • Malitsky, Y., Tam, M. K. (2020). A forward-backward splitting method for monotone inclusions without cocoercivity. SIAM Journal on Optimization, 30(2), 1451-1472.
  • Machmud, R., Wijaya, A. (2016). Behavior determinant based cervical cancer early detection with machine learning algorithm. Advanced Science Letters, 22(10), 3120-3123.
  • Osilike, M.O., Aniagbosor, S.C., Akuchu, B.G. (2002). Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, Panamerican Mathematical Journal, 12(2), 77-88.
  • Tseng, P. , A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim., 2000, 38(2), 431-446.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288.
  • Uko, L. U. (1996). Generalized equations and the generalized Newton method. Mathematical programming, 73(3), 251-268.
  • Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600-612.
  • Xu, H.K. (2010). Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Problems, 26(10), 105018.
  • Yang, Q. (2004). The relaxed CQ algorithm solving the split feasibility problem. Inverse Problems, 20(4), 1261.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Suparat Kesornprom

Prasit Cholamjiak

Publication Date December 30, 2022
Published in Issue Year 2022

Cite

APA Kesornprom, S., & Cholamjiak, P. (n.d.). A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. Results in Nonlinear Analysis, 5(4), 412-422. https://doi.org/10.53006/rna.1143531
AMA Kesornprom S, Cholamjiak P. A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. RNA. 5(4):412-422. doi:10.53006/rna.1143531
Chicago Kesornprom, Suparat, and Prasit Cholamjiak. “A Double Proximal Gradient Method With New Linesearch for Solving Convex Minimization Problem With Application to Data Classification”. Results in Nonlinear Analysis 5, no. 4 n.d.: 412-22. https://doi.org/10.53006/rna.1143531.
EndNote Kesornprom S, Cholamjiak P A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. Results in Nonlinear Analysis 5 4 412–422.
IEEE S. Kesornprom and P. Cholamjiak, “A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification”, RNA, vol. 5, no. 4, pp. 412–422, doi: 10.53006/rna.1143531.
ISNAD Kesornprom, Suparat - Cholamjiak, Prasit. “A Double Proximal Gradient Method With New Linesearch for Solving Convex Minimization Problem With Application to Data Classification”. Results in Nonlinear Analysis 5/4 (n.d.), 412-422. https://doi.org/10.53006/rna.1143531.
JAMA Kesornprom S, Cholamjiak P. A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. RNA.;5:412–422.
MLA Kesornprom, Suparat and Prasit Cholamjiak. “A Double Proximal Gradient Method With New Linesearch for Solving Convex Minimization Problem With Application to Data Classification”. Results in Nonlinear Analysis, vol. 5, no. 4, pp. 412-2, doi:10.53006/rna.1143531.
Vancouver Kesornprom S, Cholamjiak P. A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. RNA. 5(4):412-2.