Juan Guillermo Garrido
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View article: Characterization of Strong Local Maximal Monotonicity through Graphical Derivatives
Characterization of Strong Local Maximal Monotonicity through Graphical Derivatives Open
This paper is devoted to study a characterization of (strong) local maximal monotonicity in terms of a property involving the graphical derivative of a set-valued mapping defined on a Hilbert space. As a consequence, a second-order charact…
View article: Inexact Catching-Up Algorithm for Moreau's Sweeping Processes
Inexact Catching-Up Algorithm for Moreau's Sweeping Processes Open
In this paper, we develop an inexact version of the catching-up algorithm for sweeping processes. We define a new notion of approximate projection, which is compatible with any numerical method for approximating exact projections, as this …
View article: A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization
A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization Open
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The classi…
View article: Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes
Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes Open
In this paper, we develop an enhanced version of the catching-up algorithm for sweeping processes through an appropriate concept of approximate projections. We establish some properties of this notion of approximate projection. Then, under…
View article: Integral functionals on nonseparable Banach spaces with applications
Integral functionals on nonseparable Banach spaces with applications Open
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results. T…
View article: Random multifunctions as the set minimizers of infinitely many differentiable random functions
Random multifunctions as the set minimizers of infinitely many differentiable random functions Open
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…