Related papers: Finite-Time Optimization via Scaled Gradient-Momen…

We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of gradient flow iterations and…

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic…

This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain…

We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…

For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation…

We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit…

We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…

This paper studies a distributed continuous-time aggregative optimization problem, which is a fundamental problem in the price-based energy management. The objective of the distributed aggregative optimization is to minimize the sum of…

We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…

The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact…