Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification*

Chaiwino, Wipawinee; Saksuriya, Payakorn; Suparatulatorn, Raweerote

doi:10.3390/math14010101

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Open AccessFeature PaperArticle

Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*

by

Wipawinee Chaiwino

^1,2,3

,

Payakorn Saksuriya

^1,2,4

and

Raweerote Suparatulatorn

^1,2,5,*

¹

Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand

²

Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand

³

Office of Research Administration, Chiang Mai University, Chiang Mai 50200, Thailand

⁴

International College of Digital Innovation, Chiang Mai University, Chiang Mai 50200, Thailand

⁵

Department of Mathematics, Faculty of Science, Lampang Rajabhat University, Lampang 52100, Thailand

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(1), 101; https://doi.org/10.3390/math14010101 (registering DOI)

Submission received: 27 November 2025 / Revised: 19 December 2025 / Accepted: 22 December 2025 / Published: 26 December 2025

(This article belongs to the Special Issue Nonlinear Functional Analysis: Theory, Methods, and Applications)

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Abstract

This article introduces an iterative algorithm that is created by integrating the

S^{*}

-iteration process with the inertial forward-backward algorithm. The algorithm is designed to solve optimization problems formulated as variational inclusions in a real Hilbert space. We establish the weak convergence of the algorithm under conventional assumptions. One of the applications of the algorithm is to solve the extreme learning machine, which can be transformed into the variational inclusion problem. Different algorithms, with all parameters set to be identical, are employed to solve the stroke classification problem in order to evaluate the algorithm’s performance. The results indicate that our algorithm converges faster than others and achieves a precision of 93.90%, a recall of 100%, and an F1-score of 96.58%.

Keywords: variational inclusion problem; forward–backward algorithm; classification; stroke; process innovation

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MDPI and ACS Style

Chaiwino, W.; Saksuriya, P.; Suparatulatorn, R. Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*. Mathematics 2026, 14, 101. https://doi.org/10.3390/math14010101

AMA Style

Chaiwino W, Saksuriya P, Suparatulatorn R. Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*. Mathematics. 2026; 14(1):101. https://doi.org/10.3390/math14010101

Chicago/Turabian Style

Chaiwino, Wipawinee, Payakorn Saksuriya, and Raweerote Suparatulatorn. 2026. "Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*" Mathematics 14, no. 1: 101. https://doi.org/10.3390/math14010101

APA Style

Chaiwino, W., Saksuriya, P., & Suparatulatorn, R. (2026). Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*. Mathematics, 14(1), 101. https://doi.org/10.3390/math14010101

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Solving Variational Inclusion Problems with Inertial S Forward-Backward Algorithm and Application to Stroke Prediction Data Classification^*

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