Related papers: Global convergence of a modified BFGS-type method …
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
This article explores how to effectively incorporate curvature information generated using SIMD-parallel forward-mode Algorithmic Differentiation (AD) into unconstrained Quasi-Newton (QN) minimization of a smooth objective function, $f$.…
The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In…
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…
Recent control algorithms for Markov decision processes (MDPs) have been designed using an implicit analogy with well-established optimization algorithms. In this paper, we adopt the quasi-Newton method (QNM) from convex optimization to…
We study a federated version of multi-objective optimization (MOO), where a single model is trained to optimize multiple objective functions. MOO has been extensively studied in the centralized setting but is less explored in federated or…
The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since the standard L-BFGS method uses a line search to guarantee its global convergence, it sometimes requires a large…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…
Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs.…
This work studies the usage of well-known smoothed total variation regularization for solving an atmospheric tomography problem named as {\em GPS-tomography} in some quasi-Newton methods. That is we solve an unconstrained, convex, smooth…
We introduce the decentralized Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. The D-BFGS method is of interest in problems that are not well…
Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…
Non-asymptotic convergence analysis of quasi-Newton methods has gained attention with a landmark result establishing an explicit local superlinear rate of O$((1/\sqrt{t})^t)$. The methods that obtain this rate, however, exhibit a well-known…
We present two sampled quasi-Newton methods (sampled LBFGS and sampled LSR1) for solving empirical risk minimization problems that arise in machine learning. Contrary to the classical variants of these methods that sequentially build…
In this paper, we propose the first Quasi-Newton method with a global convergence rate of $O(k^{-1})$ for general convex functions. Quasi-Newton methods, such as BFGS, SR-1, are well-known for their impressive practical performance.…
We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a…