9 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.…
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…
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…
A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions
Sergio López-Rivera, Pedro Pérez-Aros, Emilio Vilches
In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear oper…