A bi-inertial Mann projective forward-backward splitting algorithm for variational inclusion problems with application to lung cancer screening
Volume 38, Issue 2, pp 201--213
https://dx.doi.org/10.22436/jmcs.038.02.04
Publication Date: December 13, 2024
Submission Date: July 27, 2024
Revision Date: September 08, 2024
Accteptance Date: October 23, 2024
Authors
P. Peeyada
- School of Science, University of Phayao, Phayao 56000, Phayao 56000, Thailand.
W. Cholamjiak
- School of Science, University of Phayao, Phayao 56000, Thailand.
K. Shiangjen
- School of Information and Communication Technology, University of Phayao, Phayao 56000, Thailand.
Abstract
This paper proposes a bi-inertial Mann projective forward-backward splitting algorithm to solve the variational inclusion problem in real Hilbert spaces. We establish a weak convergence result under mild conditions commonly used in convergence analysis. Additionally, we present a series of numerical experiments to demonstrate the efficiency of our algorithm compared to existing methods. Finally, we applied our algorithm to classify data using the lung cancer dataset, achieving the highest testing accuracy of 90.32\%, surpassing other documented algorithms. Our results indicate that the proposed algorithm offers a practical solution for detecting lung cancer.
Share and Cite
ISRP Style
P. Peeyada, W. Cholamjiak, K. Shiangjen, A bi-inertial Mann projective forward-backward splitting algorithm for variational inclusion problems with application to lung cancer screening, Journal of Mathematics and Computer Science, 38 (2025), no. 2, 201--213
AMA Style
Peeyada P., Cholamjiak W., Shiangjen K., A bi-inertial Mann projective forward-backward splitting algorithm for variational inclusion problems with application to lung cancer screening. J Math Comput SCI-JM. (2025); 38(2):201--213
Chicago/Turabian Style
Peeyada, P., Cholamjiak, W., Shiangjen, K.. "A bi-inertial Mann projective forward-backward splitting algorithm for variational inclusion problems with application to lung cancer screening." Journal of Mathematics and Computer Science, 38, no. 2 (2025): 201--213
Keywords
- Forward-backward splitting algorithm
- variational inclusion problem
- extreme learning machine
- data classification
- lung cancer dataset
MSC
References
-
[1]
Y. Alber, I. Ryazantseva, Nonlinear ill-posed problems of monotone type, Springer, Dordrecht (2006)
-
[2]
F. Alvarez, H. Attouch, An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Anal., 9 (2001), 3–11
-
[3]
H. H. Bauschke, P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, Springer, New York (2011)
-
[4]
L.-C. Ceng, Q. H. Ansari, M. M. Wong, J.-C. Yao, Mann type hybrid extragradient method for variational inequalities, variational inclusions and fixed point problems, Fixed Point Theory, 13 (2012), 403–422
-
[5]
S. Chen, D. Heng, J. Huang, Z. Chen, J Zhao, Two-step inertial adaptive iterative algorithm for solving the split common fixed point problem of directed operators, J. Nonlinear Funct. Anal., 2023 (2023), 12 pages
-
[6]
P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, 53 (2004), 475–504
-
[7]
P. L. Combettes, V. R.Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168–1200
-
[8]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge (1990)
-
[9]
N. X. Hai, P. Q. Khanh, The solution existence of general variational inclusion problems, J. Math. Anal. Appl., 328 (2007), 1268–1277
-
[10]
N.-J. Huang, A new completely general class of variational inclusions with noncompact valued mappings, Comput. Math. Appl., 35 (1998), 9–14
-
[11]
G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: Theory and applications, Neurocomputing, 70 (2006), 489–501
-
[12]
O. S. Iyiola, Y. Shehu, Convergence results of two-step inertial proximal point algorithm, Appl. Numer. Math., 182 (2022), 57–75
-
[13]
L. O. Jolaoso, Y. Shehu, J. C. Yao, R. Xu, Double inertial parameters forward-backward splitting method: Applications to compressed sensing, image processing, and SCAD penalty problems, J. Nonlinear Var. Anal., 7 (2023), 627–646
-
[14]
W. Khuangsatung, A. Kangtunyakarn, Algorithm of a new variational inclusion problem and strictly pseudononspreading mapping with application, Fixed Point Theory Appl., 2014 (2014), 27 pages
-
[15]
P.-L. Lions, B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal., 16 (1979), 964–979
-
[16]
G. López, V. Martín-Márquez, F. Wang, H.-K. Xu, Forward-backward splitting methods for accretive operators in Banach spaces, Abstr. Appl. Anal., 2012 (2012), 25 pages
-
[17]
D. A. Lorenz, T. Pock, An inertial forward-backward algorithm for monotone inclusions, J. Math. Imaging Vis., 51 (2015), 311–325
-
[18]
Y. Malitsky, M. K. Tam, A forward-backward splitting method for monotone inclusions without cocoercivity, SIAM J. Optim., 30 (2020), 1451–1472
-
[19]
G. Marino, H. K. Xu, Convergence of generalized proximal point algorithms, Commun. Pure Appl. Anal., 3 (2004), 791–808
-
[20]
G. J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J., 29 (1962), 341–346
-
[21]
N. Pakkaranang, Double inertial extragradient algorithms for solving variational inequality problems with convergence analysis, Math. Methods Appl. Sci., 47 (2024), 11642–11669
-
[22]
B. T. Polyak, Some methods of speeding up the convergence of iteration methods, USSR Comput. Math. Math. Phys., 4 (1964), 1–17
-
[23]
S. Raschka, Model evaluation, model selection, and algorithm selection in machine learning, arXiv preprint arXiv:1811.12808, (2018), 1–49
-
[24]
R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), 877–898
-
[25]
B. Tan, S. Y. Cho, Strong convergence of inertial forward–backward methods for solving monotone inclusions, Appl. Anal., 101 (2022), 5386–5414
-
[26]
B. Tan, X. Qin, On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems, Adv. Comput. Math., 50 (2024), 35 pages
-
[27]
B. Tan, X. Qin, J.-C. Yao, Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications, J. Sci. Comput., 87 (2021), 34 pages
-
[28]
R. U. Verma, A-monotonicity and applications to nonlinear variational inclusion problems, J. Appl. Math. Stoch. Anal., 2004 (2004), 193–195
-
[29]
S.-S. Zhang, J. H. W. Lee, C. K. Chan, Algorithms of common solutions to quasi variational inclusion and fixed point problems, Appl. Math. Mech. (English Ed.), 29 (2008), 571–581
-
[30]
C. Zhang, Y. Wang, Proximal algorithm for solving monotone variational inclusion, Optimization, 67 (2018), 1197–1209