Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time

• URL: http://arxiv.org/abs/2606.17260v1
• Date: Mon, 15 Jun 2026 20:07:51 GMT
• Title: Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
• Abstract summary: We develop Hamiltonian dynamics-based algorithms for smooth convex optimization.<n>We show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees.
• Score: 11.705571254663054
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated convex optimization.

Related papers

• Dynamic Anisotropic Smoothing for Noisy Derivative-Free Optimization [0.0]
  We propose a novel algorithm that extends the methods of ball smoothing and Gaussian smoothing for noisy derivative-free optimization. The algorithm dynamically adapts the shape of the smoothing kernel to approximate the Hessian of the objective function around a local optimum.
  arXiv  Detail & Related papers  (2024-05-02T21:04:20Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [61.98523595657983]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms.<n>An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Generalized Gradient Flows with Provable Fixed-Time Convergence and Fast Evasion of Non-Degenerate Saddle Points [8.452349885923507]
  Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time theory of optimal time, we introduce a framework for designing accelerated optimization algorithms. For functions that admit non-de saddle-points, we show that the time required to evade these saddle-points is uniformly bounded for all initial conditions.
  arXiv  Detail & Related papers  (2022-12-07T16:36:23Z)
• Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization [108.35402316802765]
  We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Ascent. We show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings. We extend our algorithm to extend the setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings.
  arXiv  Detail & Related papers  (2022-10-31T17:59:29Z)
• Breaking the Convergence Barrier: Optimization via Fixed-Time Convergent Flows [4.817429789586127]
  We introduce a Poly-based optimization framework for achieving acceleration, based on the notion of fixed-time stability dynamical systems. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms.
  arXiv  Detail & Related papers  (2021-12-02T16:04:40Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Acceleration Methods [57.202881673406324]
  We first use quadratic optimization problems to introduce two key families of acceleration methods. We discuss momentum methods in detail, starting with the seminal work of Nesterov. We conclude by discussing restart schemes, a set of simple techniques for reaching nearly optimal convergence rates.
  arXiv  Detail & Related papers  (2021-01-23T17:58:25Z)
• Approximate optimization of MAXCUT with a local spin algorithm [0.0]
  Local tensor methods are a class of optimization algorithms introduced in [Hastings,arXiv:1905.07047v2]. We investigate performance in practice through benchmarking experiments on instances of the MAXCUT problem. We find time to solution achieved by the local tensor method is highly uncorrelated with that achieved by a widely used commercial optimization package.
  arXiv  Detail & Related papers  (2020-08-13T18:00:00Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives [97.16266088683061]
  The article rigorously establishes why symplectic discretization schemes are important for momentum-based optimization algorithms. It provides a characterization of algorithms that exhibit accelerated convergence.
  arXiv  Detail & Related papers  (2020-02-28T00:32:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.