Single-step algorithm for variational inequality problems in 2-uniformly convex banach spaces

Bello, A. U.; Yusuf, H.; Djitte, N.

doi:10.1007/s12215-022-00746-7

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2023

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“…See, for example, [1][2][3] and references therein. In addition, under some assumptions, such problems involve many important concepts in applied mathematics, such as convex minimization, split feasibility, fixed points, saddle points, and variational inequalities; see, for example, [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A Regularized Tseng Method for Solving Various Variational Inclusion Problems and Its Application to a Statistical Learning Model

Taiwo,

Reich

2023

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We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.

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