相关论文: Enhancing structure relaxations for first-principl…

Ab initio atomic relaxations often take large numbers of steps and long times to converge. An atomic relaxation method based on on-the-flight force learning and a corresponding new curved line minimization algorithm is presented to…

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is…

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…

We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…

In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…

We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…

We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

This work investigates the acceleration of MPGP-type algorithms using preconditioning for the solution of quadratic programming problems. The preconditioning needs to be done only on the free set so as not to change the constraints. A…

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…

In stochastic zeroth-order optimization, a problem of practical relevance is understanding how to fully exploit the local geometry of the underlying objective function. We consider a fundamental setting in which the objective function is…

In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…

Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…