l-bfgs method – Optimization Online

Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

Published: 2016/07/05, Updated: 2017/05/21

Nonlinear Optimization complexity, l-bfgs method, nonconvex optimization, quasi-newton methods, stochastic approximation, stochastic optimization

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle ($\SFO$). We propose a general framework for such methods, for which we prove almost sure convergence to stationary points and analyze its worst-case … Read more

A practical method for solving large-scale TRS

Published: 2009/03/07, Updated: 2010/05/16

Marianna S. Apostolopoulou

C.A. Botsaris

Panagiotis Pintelas

Dimitris G. Sotiropoulos

Constrained Nonlinear Optimization, Nonlinear Optimization, Quadratic Programming eigenvalues, l-bfgs method, large-scale optimization, nearly exact method, negative curvature direction, trust-region methods

We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study in concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Mor\'{e}-Sorensen method that exploits the eigenstructure of … Read more