相关论文: A simple and practical adaptive trust-region metho…

Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…

We present an algorithm to perform trust-region-based optimization for nonlinear unconstrained problems. The method selectively uses function and gradient evaluations at different floating-point precisions to reduce the overall energy…

In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for…

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…

We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuous Hessian.…

We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without…

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…

We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite differences and selects the regularization…

We investigate stochastic gradient methods and stochastic counterparts of the Barzilai-Borwein steplengths and their application to finite-sum minimization problems. Our proposal is based on the Trust-Region-ish (TRish) framework introduced…

In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [Curtis2019, Curtis2022]. A theoretical analysis that complements the results…

In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…

Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos trust-region (GLTR) method is a well-known Lanczos type approach for solving a large-scale TRS. The…

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…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers…

This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the…

Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes $\mathcal{O}(\epsilon^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive…