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We study regularity properties of the subdifferential of proper lower semicontinuous convex functions in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the… (More)

- Francisco J. Aragón Artacho, Jonathan M. Borwein
- J. Global Optimization
- 2013

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex… (More)

In this paper we consider the following general version of the proximal point algorithm for solving the inclusion T (x) 3 0, where T is a set-valued mapping acting from a Banach space X to a Banach… (More)

- Francisco J. Aragón Artacho, Jonathan M. Borwein, Victoria Martín-Márquez, Liangjin Yao
- Math. Program.
- 2014

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of… (More)

- Francisco J. Aragón Artacho, Asen L. Dontchev, Michaël Gaydu, Michel H. Geoffroy, Vladimir M. Veliov
- SIAM J. Control and Optimization
- 2011

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… (More)

In this paper we give general recommendations for successful application of the Douglas–Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are… (More)

Recent positive experiences applying convex feasibility algorithms of Douglas–Rachford type to highly combinatorial and far from convex problems are described.

- Francisco J. Aragón Artacho, Ronan M. T. Fleming
- Optimization Letters
- 2015

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide… (More)

We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the… (More)

- Francisco J. Aragón Artacho, A. Belyakov, Asen L. Dontchev, Marco A. López
- Comp. Opt. and Appl.
- 2014

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden… (More)