8 papers
Metric gradient flows and variational principles
Alberto Domínguez Corella
We show that Ekeland-type variational principles can be derived from steepest descent curves in metric spaces. From this, we relate the existence of the Calabi flow to the validity…
A class of non-cylindrical domains for parabolic equations
Alberto Domínguez Corella, Jorge Rivera-Noriega
We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boun…
A note on absolutely minimal extensions in finite metric spaces
Alberto Domínguez Corella, Trí Minh Lê
Absolutely minimal Lipschitz extensions (AMLEs) are known to exist in many infinite metric settings, but the finite case is less settled. In metric spaces with at most four points,…
Viability Theory in the 1-Wasserstein Space
Benoît Bonnet-Weill, Alberto Domínguez Corella, Hélène Frankowska
In this article, we establish necessary and sufficient viability conditions for continuity inclusions over the 1-Wasserstein space. Depending on the regularity properties of the dy…
Feature weighting for data analysis via evolutionary simulation
Aris Daniilidis, Alberto Domínguez Corella, Philipp Wissgott
We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves weights (interpreted as…
A first-order condition for discrete-time distribution steering
Alberto Domínguez Corella, David González-Sánchez
We study a class of distribution-steering problems from a variational point of view. Under some differentiability assumptions, we derive necessary conditions for optimal Markov pol…
On the growth of nonconvex functionals at strict local minimizers
Alberto Domínguez Corella, Trí Minh Lê
We give new characterizations of growth conditions at strict local minimizers. The main characterizations are a variant of the so-called tilt stability property and an analog of th…
Mini-batch descent in semiflows
Alberto Domínguez Corella, Martín Hernández
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-b…