相关论文: Accelerated gradient flows for large bending defor…

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its…

In the lines of our approach in \cite{Ouorou2019}, where we exploit Nesterov fast gradient concept \cite{Nesterov1983} to the Moreau-Yosida regularization of a convex function, we devise new proximal algorithms for nonsmooth convex…

A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

This paper proposes a novel class of data-driven acceleration methods for steady-state flow field solvers. The core innovation lies in predicting and assigning the asymptotic limit value for each parameter during iterations based on its own…

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a {\em faster…

The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often performed in practice by tuning filter parameters, such as by increasing the width of the…

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…

We consider the decentralized optimization problem, where a network of $n$ agents aims to collaboratively minimize the average of their individual smooth and convex objective functions through peer-to-peer communication in a directed graph.…

In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…

Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little…

Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically…

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the…

As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…