New modification of projected reflected gradient algorithm

doi:10.1080/02331934.2025.2589368

New modification of projected reflected gradient algorithm

2025-11-01

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DOI：10.1080/02331934.2025.2589368

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This paper introduces a projected reflected gradient algorithm for solving variational inequalities in Hilbert spaces, enhanced by inertial extrapolation and self-adaptive step sizes. The inertial terms and the strategy of increasing the step size at each iteration are designed to accelerate the projected reflected gradient algorithm. We establish weak convergence of the proposed algorithm and prove linear convergence under standard conditions. Our general framework is shown to encompass a range of existing algorithms from the literature. Numerical experiments demonstrate the superior performance of our method compared to other related algorithms.

Keywords:

Variational inequalities

inertials

convergence

New modification of projected reflected gradient algorithm

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