9 papers
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.…
Sharp bounds for stochastic proximal and projection estimators via radial dominance
Gonzalo Contador, Pedro Pérez-Aros, Emilio Vilches
We study stochastic barycentric estimators for proximal points and metric projections obtained by exponentially reweighting Gaussian perturbations. Our main result is an abstract c…
Differentiability and Approximation of Probability Functions under Gaussian Mixture Models
Gonzalo Contador, Pedro Pérez-Aros, Emilio Vilches
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate G…
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…
Convergence Rates for Stochastic Proximal and Projection Estimators
Diego Morales, Pedro Pérez-Aros, Emilio Vilches
In this paper, we establish explicit convergence rates for the stochastic smooth approximations of infimal convolutions introduced and developed in \cite{MR4581306,MR4923371}. In p…
Penalty-Based Smoothing of Convex Nonsmooth Supremum Functions with Accelerated Inertial Dynamics
Samir Adly, Juan José Maulén, Emilio Vilches
We propose a penalty-based smoothing framework for convex nonsmooth functions with a supremum structure. The regularization yields a differentiable surrogate with controlled approx…