A novel neural network with predefined-time stability for solving generalized monotone inclusion problems with applications
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908793317621760 |
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| author | Van Tran, Nam |
| author_facet | Van Tran, Nam |
| contents | We propose a novel dynamical framework for solving inclusion
problems of the form \(0 \in F(x) + G(x)\) in Hilbert spaces, where \(F\) is a
maximal set-valued operator and \(G\) is a single-valued mapping. The analysis is
conducted under a generalized monotonicity assumption, which relaxes the
classical monotonicity conditions commonly imposed in the literature and thereby
extends the applicability of the proposed approach.
Under mild conditions on the system parameters, we establish both fixed-time and
predefined-time stability of the resulting dynamical system. The fixed-time
stability guarantees a uniform upper bound on the settling time that is
independent of the initial condition, whereas the predefined-time stability
framework allows the system parameters to be selected \emph{a priori} in order
to ensure convergence within a user-specified time horizon.
Moreover, we investigate an explicit forward Euler discretization of the
continuous-time dynamics, leading to a novel forward--backward iterative
algorithm. A rigorous convergence analysis of the resulting discrete scheme is
provided. Finally, the effectiveness and versatility of the proposed method are
illustrated through several classes of problems, including constrained
optimization problems, mixed variational inequalities, and variational
inequalities, together with numerical experiments that corroborate the
theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A novel neural network with predefined-time stability for solving generalized monotone inclusion problems with applications Van Tran, Nam Optimization and Control We propose a novel dynamical framework for solving inclusion problems of the form \(0 \in F(x) + G(x)\) in Hilbert spaces, where \(F\) is a maximal set-valued operator and \(G\) is a single-valued mapping. The analysis is conducted under a generalized monotonicity assumption, which relaxes the classical monotonicity conditions commonly imposed in the literature and thereby extends the applicability of the proposed approach. Under mild conditions on the system parameters, we establish both fixed-time and predefined-time stability of the resulting dynamical system. The fixed-time stability guarantees a uniform upper bound on the settling time that is independent of the initial condition, whereas the predefined-time stability framework allows the system parameters to be selected \emph{a priori} in order to ensure convergence within a user-specified time horizon. Moreover, we investigate an explicit forward Euler discretization of the continuous-time dynamics, leading to a novel forward--backward iterative algorithm. A rigorous convergence analysis of the resulting discrete scheme is provided. Finally, the effectiveness and versatility of the proposed method are illustrated through several classes of problems, including constrained optimization problems, mixed variational inequalities, and variational inequalities, together with numerical experiments that corroborate the theoretical results. |
| title | A novel neural network with predefined-time stability for solving generalized monotone inclusion problems with applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.20338 |