References of "Gaydu, M"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailA Lyusternik - Graves theorem for the proximal point method
Aragón Artacho, Francisco Javier UL; Gaydu, M.

in Computational Optimization and Applications (2012), 52(3), 785-803

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach ... [more ▼]

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (x̅,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular. [less ▲]

Detailed reference viewed: 60 (5 UL)
Full Text
Peer Reviewed
See detailMetric regularity of Newton's iteration
Aragón Artacho, Francisco Javier UL; Dontchev, A. L.; Gaydu, M. et al

in SIAM Journal on Control & Optimization (2011), 49(2), 339-362

For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik–Graves theorem to the framework of a mapping acting from the pair “parameter ... [more ▼]

For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik–Graves theorem to the framework of a mapping acting from the pair “parameter-starting point” to the set of corresponding convergent Newton sequences. Under ample parameterization, metric regularity of the mapping associated with convergent Newton sequences becomes equivalent to the metric regularity of the mapping associated with the generalized equation. We also discuss an inexact Newton method and present an application to discretized optimal control. [less ▲]

Detailed reference viewed: 61 (7 UL)