proximal quasi-newton method – Optimization Online

An Inexact Modified Quasi-Newton Method for Nonsmooth Regularized Optimization

Published: 2026/01/05

We introduce method iR2N, a modified proximal quasi-Newton method for minimizing the sum of a \(C^1\) function \(f\) and a lower semi-continuous prox-bounded \(h\) that permits inexact evaluations of \(f\), \(\nabla f\) and of the relevant proximal operators. Both \(f\) and \(h\) may be nonconvex. In applications where the proximal operator of \(h\) is not … Read more

A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization

Published: 2021/03/30, Updated: 2021/08/19

Aleksandr Y. Aravkin

Robert Baraldi

Dominique Orban

Nonlinear Optimization, Nonsmooth Optimization composite optimization, nonconvex optimization, nonsmooth optimization, proximal gradient method, proximal quasi-newton method, quasi-newton methods, regularized optimization, trust-region methods

We develop a trust-region method for minimizing the sum of a smooth term f and a nonsmooth term h, both of which can be nonconvex. Each iteration of our method minimizes apossibly nonconvex model of f+h in a trust region. The model coincides with f+h in value and subdifferential at the center. We establish global … Read more