A perturbed convex combination method for pseudo-monotone variational inequalities with applications to blood supply chain networks

Ghaziyah Alsahli; Sani Salisu; Nura Alotaibi; Ghaziyah Alsahli; Sani Salisu; Nura Alotaibi

doi:10.3934/math.20261014

AIMS Mathematics

2026, Volume 11, Issue 8: 25229-25264. doi: 10.3934/math.20261014

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Research article

A perturbed convex combination method for pseudo-monotone variational inequalities with applications to blood supply chain networks

1.
Department of Mathematics, College of Sciences, Jouf University, Sakaka, P.O. Box 2014, Saudi Arabia
2.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
3.
Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University, Kafin Hausa, Jigawa, Nigeria

Received: 22 January 2026 Revised: 31 March 2026 Accepted: 14 April 2026 Published: 14 August 2026
MSC : 47H05, 49J40, 49M37, 90B50, 90C25, 90C30

The paper proposes a new adaptive algorithm for solving variational inequality problems (VIPs) with pseudo-monotone operators. Such problems are central to modeling equilibrium in supply chain networks, where asymmetric cost structures lead to pseudo-monotonicity. The proposed method integrates convex combination techniques with an adaptive step-size criterion, requiring only a single metric projection per iteration. We prove linear convergence under strong pseudo-monotonicity and weak convergence under pseudo-monotonicity. Numerical experiments on a blood supply chain network with 24 routes and three demand scenarios show that the algorithm performs competitively with recent methods in terms of residual reduction and achieves the lowest execution time. The results demonstrate the algorithm's efficiency and scalability for large-scale network optimization, with potential impact on healthcare logistics and related applications.
- variational inequality,
- adaptive algorithm,
- supply chain network,
- pseudo-monotone,
- convex combination,
- linear convergence rate
Citation: Ghaziyah Alsahli, Sani Salisu, Nura Alotaibi. A perturbed convex combination method for pseudo-monotone variational inequalities with applications to blood supply chain networks[J]. AIMS Mathematics, 2026, 11(8): 25229-25264. doi: 10.3934/math.20261014

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Abstract

The paper proposes a new adaptive algorithm for solving variational inequality problems (VIPs) with pseudo-monotone operators. Such problems are central to modeling equilibrium in supply chain networks, where asymmetric cost structures lead to pseudo-monotonicity. The proposed method integrates convex combination techniques with an adaptive step-size criterion, requiring only a single metric projection per iteration. We prove linear convergence under strong pseudo-monotonicity and weak convergence under pseudo-monotonicity. Numerical experiments on a blood supply chain network with 24 routes and three demand scenarios show that the algorithm performs competitively with recent methods in terms of residual reduction and achieves the lowest execution time. The results demonstrate the algorithm's efficiency and scalability for large-scale network optimization, with potential impact on healthcare logistics and related applications.

References

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