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ICMRA Seminar Series
ICMRA Seminar Series
Double Inertial Golden Ratio Methods for Variational Inequalities in Hilbert Spaces
Double Inertial Golden Ratio Methods for Variational Inequalities in Hilbert Spaces
Organizers
Speaker
Godwin Chidi Ugwunnadi
Time
Monday, June 22, 2026 3:30 PM - 4:30 PM
Venue
A6-101
Online
Zoom 204 323 0165
(BIMSA)
Abstract
Variational inequalities provide a powerful unifying framework for optimization, equilibrium problems, and many applications in engineering and data science. In this talk, we begin by introducing the classical variational inequality problem and show how it naturally arises from the minimization of a differentiable convex function. Using the fundamental properties of metric projection, we derive the projection method one of the most basic iterative schemes for solving VIPs. We then compare this approach with the well known gradient descent method in machine learning, highlighting their structural similarities and differences. We discuss the limitations of the classical projection method, particularly its reliance on strong monotonicity and its slow convergence, and review key extensions developed to overcome these challenges.
We then present a Double Inertial Golden Ratio Method for solving variational inequality problems with non-Lipschitz pseudomonotone operators in Hilbert spaces. The algorithm integrates subgradient and extragradient techniques with Armijo-type line search, double inertial steps, and the golden ratio mechanism to accelerate convergence and stabilize extrapolation. We establish weak convergence under general pseudomonotonicity and R-linear convergence under strong pseudomonotonicity. Numerical experiments demonstrate that the proposed method significantly outperforms existing algorithms.
Beyond the theoretical framework, the method is currently being applied to image restoration, least squares problems, and LASSO problems in machine learning and signal processing. Future work will extend these results to reflexive Banach spaces using Bregman divergence techniques and explore broader real-world applications.
We then present a Double Inertial Golden Ratio Method for solving variational inequality problems with non-Lipschitz pseudomonotone operators in Hilbert spaces. The algorithm integrates subgradient and extragradient techniques with Armijo-type line search, double inertial steps, and the golden ratio mechanism to accelerate convergence and stabilize extrapolation. We establish weak convergence under general pseudomonotonicity and R-linear convergence under strong pseudomonotonicity. Numerical experiments demonstrate that the proposed method significantly outperforms existing algorithms.
Beyond the theoretical framework, the method is currently being applied to image restoration, least squares problems, and LASSO problems in machine learning and signal processing. Future work will extend these results to reflexive Banach spaces using Bregman divergence techniques and explore broader real-world applications.