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math.OC2026
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.…
math.OC2026
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…
math.PR2026
Stochastic Perturbation of Sweeping Processes Driven by Continuous Uniformly Prox-Regular Moving Sets
Juan Guillermo Garrido, Nabil Kazi-Tani, Emilio Vilches
In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and v…