# A Globally Convergent Proximal Newton-Type Method in Nonsmooth Convex Optimization

arXiv: https://arxiv.org/abs/2011.08166 · HTML: https://mlsanity.com/paper/2011.08166/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition](https://mlsanity.com/paper/2204.14067/) (2022)
- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)
- [Alternating Iteratively Reweighted ℓ1 and Subspace Newton Algorithms for Nonconvex Sparse Optimization](https://mlsanity.com/paper/2407.17216/) (2024)

## Abstract (arXiv)

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 variational analysis, we establish implementable results on the global convergence of the proposed algorithm as well as its local convergence with superlinear and quadratic rates. For certain structured problems, the obtained local convergence conditions do not require the local Lipschitz continuity of the corresponding Hessian mappings that is a crucial assumption used in the literature to ensure a superlinear convergence of other algorithms of the proximal Newton type. The conducted numerical experiments of solving the l1 regularized logistic regression model illustrate the possibility of applying the proposed algorithm to deal with practically important problems.