10 papers
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…
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.…
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…
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…
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…
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…
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…
Splitting Algorithms for Distributionally Robust Optimization
Luis Briceño-Arias, Sergio López-Rivera, Emilio Vilches
In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distribut…