A two-term inertial method for monotone VIPs: Implementation in multiclass classification and portfolio optimization

Zheng Jia, Jian-Wen Peng, Sani Salisu and Yekini Shehu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 510-532

Abstract: We develop a computationally efficient two-term inertial projected gradient method for monotone variational inequalities in real Hilbert spaces. Each iteration involves a single projection and one operator evaluation, ensuring low cost. The framework generalizes several existing methods, including the projected reflected gradient algorithm. A weak convergence guarantee is provided under standard conditions, alongside a linear convergence rate for strongly monotone operators. Simulations on classification and portfolio optimization demonstrate the algorithm’s competitive performance compared to existing approaches.

Keywords: Variational inequalities; Projected gradient-type method; Weak convergence; Linear rate; Hilbert spaces (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:510-532

DOI: 10.1016/j.matcom.2026.06.001

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