Related papers: Novel Limited Memory Quasi-Newton Methods Based On…

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

In this paper, a modified BFGS algorithm is proposed. The modified BFGS matrix estimates a modified Hessian matrix which is a convex combination of an identity matrix for the steepest descent algorithm and a Hessian matrix for the Newton…

In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…

Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…

L-BFGS is the state-of-the-art optimization method for many large scale inverse problems. It has a small memory footprint and achieves superlinear convergence. The method approximates Hessian based on an initial approximation and an update…

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a…

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized…

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

The Trust Region Subproblem is a fundamental optimization problem that takes a pivotal role in Trust Region Methods. However, the problem, and variants of it, also arise in quite a few other applications. In this article, we present a…

In this paper, based on function information, we propose a modified BFGS-type method for nonconvex multiobjective optimization problems (MFQNMO). In the multiobjective quasi-Newton method (QNMO), each iteration involves separately…

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or…

This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…

We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact…

Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…