相关论文: Error Inhibiting Block One-Step Schemes for Ordina…

Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…

We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…

In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when…

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…

The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…

Restricting randomization in the design of experiments (e.g., using blocking/stratification, pair-wise matching, or rerandomization) can improve the treatment-control balance on important covariates and therefore improve the estimation of…

This paper presents a sequence of deferred correction (DC) schemes built recursively from the implicit midpoint scheme for the numerical solution of general first order ordinary differential equations (ODEs). It is proven that each scheme…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…

In this paper, a new implicit-explicit local method with an arbitrary order is produced for stiff initial value problems. Here, a general method for one-step time integrations has been created, considering a direction free approach for…

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…

This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…

Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…

The objective of this paper is to prove the convergence of a linear implicit multi-step numerical method for ordinary differential equations. The algorithm is obtained via Taylor approximations. The convergence is proved following the…

A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is obtained by natural modifications of the well-known leapfrog method, which is a second order,…

Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

Although the distributed machine learning methods can speed up the training of large deep neural networks, the communication cost has become the non-negligible bottleneck to constrain the performance. To address this challenge, the gradient…