Related papers: Limited-Memory BFGS with Displacement Aggregation
A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein "two-point step size" strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the…
We propose a new stochastic variance-reduced damped L-BFGS algorithm, where we leverage estimates of bounds on the largest and smallest eigenvalues of the Hessian approximation to balance its quality and conditioning. Our algorithm,…
The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex…
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key…
In this paper, a communication-efficient federated learning (FL) framework is proposed for improving the convergence rate of FL under a limited uplink capacity. The central idea of the proposed framework is to transmit the values and…
Large language models (LLMs) can memorize and reproduce training sequences verbatim -- a tendency that undermines both generalization and privacy. Existing mitigation methods apply interventions uniformly, degrading performance on the…
The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the…
There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…
This paper addresses the equal circle packing problem, and proposes an efficient Quasi-physical Quasi-human (QPQH) algorithm. QPQH is based on a modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm which we call the local BFGS and a…
In federated learning (FL), the significant communication overhead due to the slow convergence speed of training the global model poses a great challenge. Specifically, a large number of communication rounds are required to achieve the…
In federated learning (FL), a number of devices train their local models and upload the corresponding parameters or gradients to the base station (BS) to update the global model while protecting their data privacy. However, due to the…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…
We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…
We propose a distributed bundle adjustment (DBA) method using the exact Levenberg-Marquardt (LM) algorithm for super large-scale datasets. Most of the existing methods partition the global map to small ones and conduct bundle adjustment in…