Emilio Vilches
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View article: Effects of Willow and Pine tree growth in bacterial abundance, interactions and metabolic profile in a copper mine tailing
Effects of Willow and Pine tree growth in bacterial abundance, interactions and metabolic profile in a copper mine tailing Open
The Cauquenes tailings is one of the largest mine tailings in Chile and represents a significant environmental hazard due to its high copper levels and acidic pH. However, there is evidence of willow and pine tree growth in these terrains,…
View article: A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions
A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions Open
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 operator on a closed vector subspace. For this problem, we prop…
View article: Inexact Catching-Up Algorithm for Moreau's Sweeping Processes
Inexact Catching-Up Algorithm for Moreau's Sweeping Processes Open
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 numerical method for approximating exact projections, as this …
View article: A fixed-point approach to history-dependent sweeping processes
A fixed-point approach to history-dependent sweeping processes Open
In this paper, we study the well-posedness of state-dependent and state-independent sweeping processes driven by prox-regular sets and perturbed by a history-dependent operator. Our approach, based on an enhanced version of Gronwall's lemm…
View article: A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization
A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization Open
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 Lipschitz function, both potentially nonsmooth. The classi…
View article: Differentiability and Approximation of Probability Functions under Gaussian Mixture Models: A Bayesian Approach
Differentiability and Approximation of Probability Functions under Gaussian Mixture Models: A Bayesian Approach Open
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 Gaussian random vectors to the context of Gaussian mixture m…
View article: Splitting Algorithms for Distributionally Robust Optimization
Splitting Algorithms for Distributionally Robust Optimization Open
In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity ope…
View article: Profiling extremophile bacterial communities recovered from a mining tailing against soil ecosystems through comparative genome-resolved metagenomics and evolutionary analysis
Profiling extremophile bacterial communities recovered from a mining tailing against soil ecosystems through comparative genome-resolved metagenomics and evolutionary analysis Open
Microbial communities inhabiting mining environments harbor a diverse array of bacteria with specialized metabolic capacities adapted to extreme conditions. Here, we utilized comparative genome-resolved metagenomics of a high-quality Illum…
View article: Well-posedness for integro-differential sweeping processes of Volterra type
Well-posedness for integro-differential sweeping processes of Volterra type Open
In this paper, we study the well-posedness of integro-differential sweeping processes of Volterra type. Using new enhanced versions of Gronwall's inequality, a reparametrization technique, and a fixed point argument for history-dependent o…
View article: Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes
Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes Open
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 properties of this notion of approximate projection. Then, under…
View article: Time Periodic Solutions to the Evolutionary Oseen Model for a Generalized Newtonian Incompressible Fluid
Time Periodic Solutions to the Evolutionary Oseen Model for a Generalized Newtonian Incompressible Fluid Open
View article: Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes
Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes Open
In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which…
View article: Inner Moreau envelope of nonsmooth conic chance constrained optimization problems
Inner Moreau envelope of nonsmooth conic chance constrained optimization problems Open
Optimization problems with uncertainty in the constraints occur in many applications. Particularly, probability functions present a natural form to deal with this situation. Nevertheless, in some cases, the resulting probability functions …
View article: Hamilton-Jacobi-Bellman Approach for Optimal Control Problems of Sweeping Processes
Hamilton-Jacobi-Bellman Approach for Optimal Control Problems of Sweeping Processes Open
View article: Integral functionals on nonseparable Banach spaces with applications
Integral functionals on nonseparable Banach spaces with applications Open
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 multifunctions for which we obtain measurable selection results. T…
View article: Moreau–Yosida Regularization of Degenerate State-Dependent Sweeping Processes
Moreau–Yosida Regularization of Degenerate State-Dependent Sweeping Processes Open
View article: Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities
Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities Open
In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a…
View article: Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction
Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction Open
We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger convergence. Then we present an application to…
View article: Optimal control of an evolution hemivariational inequality involving history-dependent operators
Optimal control of an evolution hemivariational inequality involving history-dependent operators Open
View article: Random multifunctions as the set minimizers of infinitely many differentiable random functions
Random multifunctions as the set minimizers of infinitely many differentiable random functions Open
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 the convexity of the random multifunction. We provide several…
View article: Moreau-Yosida Regularization of Degenerate State-Dependent Sweeping Processes
Moreau-Yosida Regularization of Degenerate State-Dependent Sweeping Processes Open
In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively $α$-far). Based on the Moreau-Yosida regularization, we prove the existence of solutions under the Li…
View article: Stabilization of periodic sweeping processes and asymptotic average\n velocity for soft locomotors with dry friction
Stabilization of periodic sweeping processes and asymptotic average\n velocity for soft locomotors with dry friction Open
We study the asymptotic stability of periodic solutions for sweeping\nprocesses defined by a polyhedron with translationally moving faces. Previous\nresults are improved by obtaining a stronger $W^{1,2}$ convergence. Then we\npresent an ap…
View article: Well-Posedness of History/State-Dependent Implicit Sweeping Processes
Well-Posedness of History/State-Dependent Implicit Sweeping Processes Open
View article: Determination of convex functions via subgradients of minimal norm
Determination of convex functions via subgradients of minimal norm Open
View article: Proximal determination of convex functions
Proximal determination of convex functions Open
We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity…
View article: Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets
Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets Open
In this paper, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prove the well-posedness and the strong convergence of the prop…
View article: An enhanced Baillon-Haddad theorem for convex functions on convex sets
An enhanced Baillon-Haddad theorem for convex functions on convex sets Open
The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is $β$-Lipschitz if and only if it is $1/β$-cocoercive. In this paper, we extend this theorem to Gâtea…
View article: On smoothness of solutions to projected differential equations
On smoothness of solutions to projected differential equations Open
Projected differential equations are known as fundamental mathematical models in economics, for electric circuits, etc. The present paper studies the (higher order) derivability as well as a generalized type of derivability of solutions of…
View article: Existence and Lyapunov Pairs for the Perturbed Sweeping Process Governed by a Fixed Set
Existence and Lyapunov Pairs for the Perturbed Sweeping Process Governed by a Fixed Set Open
View article: Lyapunov pairs for perturbed sweeping processes
Lyapunov pairs for perturbed sweeping processes Open