8 papers · 1 filter
Integral Formulation and the Brézis-Ekeland-Nayroles-Type Principle for Prox-Regular Sweeping Processes
Juan Guillermo Garrido, Emilio Vilches
We study sweeping processes in a Hilbert space driven by time-dependent uniformly prox-regular sets, allowing the moving constraint to exhibit discontinuities of bounded variation.…
Stochastic Differential Inclusions driven by Maximal Monotone Operators with empty interiors
Juan Guillermo Garrido, Pedro Pérez-Aros, Mathias Staudigl
This paper studies the long-time behavior of stochastic differential inclusions driven by maximal monotone operators, motivated by continuous-time models of first-order optimizatio…
Characterization of Strong Local Maximal Monotonicity through Graphical Derivatives
Juan Guillermo Garrido
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 o…
Inexact Catching-Up Algorithm for Moreau's Sweeping Processes
Juan Guillermo Garrido, Maximiliano Lioi, Emilio Vilches
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 num…
A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization
Juan Guillermo Garrido, Pedro Pérez-Aros, Emilio Vilches
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…
Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes
Juan Guillermo Garrido, Emilio Vilches
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 prope…
Integral functionals on nonseparable Banach spaces with applications
Juan Guillermo Garrido, Pedro Pérez-Aros, Emilio Vilches
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 multifu…
Random multifunctions as the set minimizers of infinitely many differentiable random functions
Juan Guillermo Garrido, Pedro Pérez-Aros, Emilio Vilches
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 th…