Nam V. Tran, Hai T. T. Le, A dynamical system approach with finite-time stability for solving generalized monotone inclusion without maximality

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DOI: 10.23952/asvao.6.2024.3.09
Volume 6, Issue 3, 1 December 2024, Pages 371-383

Abstract. In this paper, we introduce a forward-backward splitting dynamical system designed to address the inclusion problem of the form $0\in G(x)+F(x)$ , where $G$ is a multi-valued operator and $F$ is a single-valued operator in Hilbert spaces. The involved operators are required to satisfy a generalized monotonicity condition, which is less restrictive than standard monotone assumptions. Also, the maximality property does not impose on our involved operators. With mild conditions on parameters, we demonstrate the finite-time stability of the proposed dynamical system. We also present some applications to other optimization problems, such as Constrained Optimization Problems (COPs), Mixed Variational Inequalities (MVIs), and Variational Inequalities (VIs).

How to Cite this Article:
N.V. Tran, H.T.T. Le, A dynamical system approach with finite-time stability for solving generalized monotone inclusion without maximality, Appl. Set-Valued Anal. Optim. 6 (2024), 371-383.