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Block Proximal Point Method for Mixed Variational Inequality Problem
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DOI：10.1016/j.cnsns.2026.110786.png)
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Abstract
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Mixed variational inequalities (MVIs) offer a powerful framework for modeling various optimization and equilibrium problems in economics, engineering, and machine learning. However, solving large-scale MVIs remains computationally expensive because of their high-dimensionality and complex operator structures. This paper introduces an accelerated block proximal point algorithm that combines block decomposition and perturbed gradient directions to address these problems. By dynamically updating subsets of variables and incorporating perturbed gradient steps, our method significantly reduces per-iteration costs while maintaining convergence properties. We establish convergence under standard monotonicity and Lipschitz continuity assumptions and illustrate its effectiveness through numerical experiments on Nash-Cournot equilibrium, quadratic coupling, and financial portfolio optimization. Empirical results reveal that partial block activation achieves a favorable trade-off between accuracy and computational efficiency, making the algorithm particularly suitable for real-world applications with resource constraints.
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