Newton's method for solving generalized equations without Lipschitz condition

J Wang, W Ouyang - Journal of Optimization Theory and Applications, 2022 - Springer
This paper aims to establish higher order convergence of the (inexact) Newton's method for
solving generalized equations composed of the sum of a single-valued mapping and a set …

On Newton's method for solving generalized equations

OP Ferreira, C Jean-Alexis, A Piétrus, GN Silva - Journal of Complexity, 2023 - Elsevier
In this paper, we study the convergence properties of a Newton-type method for solving
generalized equations under a majorant condition. To this end, we use a contraction …

Extending the Rademacher Theorem to Set-Valued Maps

A Daniilidis, M Quincampoix - SIAM Journal on Optimization, 2024 - SIAM
The Rademacher theorem asserts that Lipschitz continuous functions between Euclidean
spaces are differentiable almost everywhere. In this work we extend this result to set-valued …

A General Iterative Procedure for Solving Nonsmooth Constrained Generalized Equations

W Ouyang, K Mei - Mathematics, 2023 - mdpi.com
In this paper, we concentrate on an abstract iterative procedure for solving nonsmooth
constrained generalized equations. This procedure employs both the property of weak point …

Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds

MS Louzeiro, GN Silva, J Yuan, D Zhang - arXiv preprint arXiv:2303.10554, 2023 - arxiv.org
The convergence of inexact Newton methods is studied for solving generalized equations
on Riemannian manifolds by using the metric regularity property, which is also explored …