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

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

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.

Suggested Citation

  • Jia, Zheng & Peng, Jian-Wen & Salisu, Sani & Shehu, Yekini, 2026. "A two-term inertial method for monotone VIPs: Implementation in multiclass classification and portfolio optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 510-532.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:510-532
    DOI: 10.1016/j.matcom.2026.06.001
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