Related papers: Accelerated Dinkelbach method
Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and…
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 article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases.…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
This paper presents a novel backtracking strategy for additive Schwarz methods for general convex optimization problems as an acceleration scheme. The proposed backtracking strategy is independent of local solvers, so that it can be applied…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness…
The fractional Laplacian $(-\Delta)^{\alpha/2}$ is a non-local operator which depends on the parameter $\alpha$ and recovers the usual Laplacian as $\alpha \to 2$. A numerical method for the fractional Laplacian is proposed, based on the…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…