Nonlinear three-operator splitting algorithms with momentum for monotone inclusions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917088269959168 |
|---|---|
| author | Qin, Liqian Gibali, Aviv Zhang, Cuijie Tang, Yuchao |
| author_facet | Qin, Liqian Gibali, Aviv Zhang, Cuijie Tang, Yuchao |
| contents | In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflected-backward splitting algorithm, the semi-reflected-forward-backward splitting algorithm, and the outer reflected forward-backward splitting algorithm by incorporating a nonlinear momentum term. Under appropriate step-size conditions, we establish the weak convergence of all three algorithms, and further prove their $R$-linear convergence rates under strong monotonicity assumptions. Preliminary numerical experiments on both synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear three-operator splitting algorithms with momentum for monotone inclusions Qin, Liqian Gibali, Aviv Zhang, Cuijie Tang, Yuchao Optimization and Control 47H05, 65K15, 90C25 In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflected-backward splitting algorithm, the semi-reflected-forward-backward splitting algorithm, and the outer reflected forward-backward splitting algorithm by incorporating a nonlinear momentum term. Under appropriate step-size conditions, we establish the weak convergence of all three algorithms, and further prove their $R$-linear convergence rates under strong monotonicity assumptions. Preliminary numerical experiments on both synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithms. |
| title | Nonlinear three-operator splitting algorithms with momentum for monotone inclusions |
| topic | Optimization and Control 47H05, 65K15, 90C25 |
| url | https://arxiv.org/abs/2511.14050 |