6 papers
Poly and Raby's theorem splits in infinite dimensions
David Salas
A classic result of Poly and Raby \cite{Poly-Raby:1984} states that, in finite-dimensional Euclidean spaces, -smoothness (with ) of the squared distance func…
The reach and limits of slope eikonal equations in compact spaces
David Salas, Sebastián Tapia-García, Francisco Venegas M
It is a well known fact that the eikonal equation is well posed in complete length spaces. Among the studied notions of solutions in the literature, there is one that can be define…
Metric compatibility and determination in complete metric spaces
Aris Daniilidis, Tri Minh Le, David Salas
It was established in [8] that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result,…
Descent modulus and applications
Aris Daniilidis, Laurent Miclo, David Salas
The norm of the gradient f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dis…
Exploiting the polyhedral geometry of stochastic linear bilevel programming
Gonzalo Muñoz, David Salas, Anton Svensson
We study linear bilevel programming problems whose lower-level objective is given by a random cost vector with known distribution. We consider the case where this distribution is n…
Determination of functions by metric slopes
Aris Daniilidis, David Salas
We show that in a metric space, any continuous function with compact sublevel sets and finite metric slope is uniquely determined by the slope and its critical values.