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- Title
A DYNAMICAL SYSTEM APPROACH WITH FINITE-TIME STABILITY FOR SOLVING GENERALIZED MONOTONE INCLUSION WITHOUT MAXIMALITY.
- Authors
TRAN, NAM V.; LE, HAI T. T.
- Abstract
In this paper, we introduce a forward-backward splitting dynamical system designed to address the inclusion problem of the form 0 ∈ 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).
- Subjects
FINITE element method; MONOTONE operators; OPERATOR theory; VARIATIONAL inequalities (Mathematics); CALCULUS of variations
- Publication
Applied Set-Valued Analysis & Optimization, 2024, Vol 6, Issue 3, p371
- ISSN
2562-7775
- Publication type
Article
- DOI
10.23952/asvao.6.2024.3.09