Skip to content
DraconiticResearch
Search Sources API
178,970 studies31 sourcesUpdated 32 min ago
PreprintarXiv licencearXiv

Inertial Primal-Dual Dynamics Methods Featuring Implicit Hessian-Driven Damping for Convex Optimization Problems in Continuous and Discrete Time

  • Xiangkai Sun
  • Zeying Gao
  • Liang He
  • Kok Lay Teo
Open at sourcePDFDOICite

Abstract

This paper investigates inertial primal-dual dynamics with implicit Hessian-driven damping for strongly convex optimization problems with linear equality constraints. We first establish fast convergence rates for the objective function value error, the feasibility measure, and both the trajectory and its corresponding velocity vector. By appropriately adjusting parameters, we show that the proposed system achieves exponential convergence rates. Through implicit time discretization of the dynamical system, we derive an inertial accelerated primal-dual algorithm for solving the strongly convex optimization problems. Using Lyapunov-based method, we show that the proposed algorithm achieves convergence rates consistent with those of its continuous-time counterpart. We also extend the obtained results to non-smooth convex optimization case. Furthermore, we conduct numerical experiments to illustrate theoretical results.

Related

  1. Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise
    Andreea Negruţ, Aurel Răşcanu, Eduard Rotenstein
    arXivPreprintCC BY-NC-ND 4.0Full textDynamical systemsProbabilityarXiv
  2. Optimization of a Perturbed Implicit Sweeping Process by Constrained Discontinuous Controls
    Yen Dang, Boris S. Mordukhovich, Dao Nguyen
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  3. Fully First-Order Optimization for Implicit Multilevel Compositions via Recursive Perturbations
    Xiaoyu Wang, Shiqian Ma
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  4. SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
    Viktor Stein, Levin Maier, Wuchen Li +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  5. Order elevation of directly self-starting sub-step implicit integrators for transient dynamics
    Jinze Li, Yaokun Liu, Kewei Chen +2
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingComputational physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{sun2026inertial,
  title = {{Inertial Primal-Dual Dynamics Methods Featuring Implicit Hessian-Driven Damping for Convex Optimization Problems in Continuous and Discrete Time}},
  author = {Xiangkai Sun and Zeying Gao and Liang He and Kok Lay Teo},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.25519},
  eprint = {2608.25519},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.25519},
}
RIS
TY  - UNPB
TI  - Inertial Primal-Dual Dynamics Methods Featuring Implicit Hessian-Driven Damping for Convex Optimization Problems in Continuous and Discrete Time
AU  - Xiangkai Sun
AU  - Zeying Gao
AU  - Liang He
AU  - Kok Lay Teo
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.25519
UR  - https://arxiv.org/abs/2608.25519
AB  - This paper investigates inertial primal-dual dynamics with implicit Hessian-driven damping for strongly convex optimization problems with linear equality constraints. We first establish fast convergence rates for the objective function value error, the feasibility measure, and both the trajectory and its corresponding velocity vector. By appropriately adjusting parameters, we show that the proposed system achieves exponential convergence rates. Through implicit time discretization of the dynamical system, we derive an inertial accelerated primal-dual algorithm for solving the strongly convex optimization problems. Using Lyapunov-based method, we show that the proposed algorithm achieves convergence rates consistent with those of its continuous-time counterpart. We also extend the obtained results to non-smooth convex optimization case. Furthermore, we conduct numerical experiments to illustrate theoretical results.
ER  -