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 …
solving generalized equations composed of the sum of a single-valued mapping and a set …
On Newton's method for solving generalized equations
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 …
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 …
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 …
constrained generalized equations. This procedure employs both the property of weak point …
Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
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 …
on Riemannian manifolds by using the metric regularity property, which is also explored …