arXiv subjects

Emilio Vilches

Publications and source records attributed to Emilio Vilches.

24 records · Page 2Linked to original sources

arXiv2021

Random multifunctions as the set minimizers of infinitely many differentiable random functions

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 applications of this result to the approximation of random multifunctions and integrands. The paper ends with a characterization of the set of integrable selections of a measurable multifunction as the set of minimizers of an infinitely many differentiable integral function.

math.OC↗

arXiv2021

Moreau-Yosida Regularization of Degenerate State-Dependent Sweeping Processes

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 Lipschitzianity of the moving sets with respect to the truncated Hausdorff distance.

math.OC↗

arXiv2021

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

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 $W^{1,2}$ convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.

math.DS↗

arXiv2020

Proximal determination of convex functions

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 in terms of the proximal operator is given.

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arXiv2020

Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets

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 proposed dynamical systems to a fixed point of the non-expansive operator. We apply the obtained result to dynamical system associated with the problem of finding the zeros of the sum of a cocoercive operator with the subdifferential of a convex function.

math.OC↗

arXiv2019

An enhanced Baillon-Haddad theorem for convex functions on convex sets

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 Gâteaux differentiable convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of $C^{1,+}$ convex functions in terms of local cocoercitivity.

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