7 citations · 29 across the 16 of their papers we have counts for
18 papers
Sufficient conditions for the absence of relaxation gaps in state-constrained optimal control
Nicolas Augier, Milan Korda, Rodolfo Rios-Zertuche
This work presents new sufficient conditions for the absence of a gap corresponding to Young measure and occupation measure relaxations for constrained optimal control problems. Un…
Young measure relaxation gaps for controllable systems with smooth state constraints
Nicolas Augier, Milan Korda, Rodolfo Rios-Zertuche
In this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexam…
Convergence rates for sums-of-squares hierarchies with correlative sparsity
Milan Korda, Victor Magron, Rodolfo Rios-Zertuche
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semi…
Occupation measure relaxations in variational problems: the role of convexity
Didier Henrion, Milan Korda, Martin Kružík +1
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming relaxation amenable to numerical appro…
The gap between a variational problem and its occupation measure relaxation
Milan Korda, Rodolfo Rios-Zertuche
Recent works have proposed linear programming relaxations of variational optimization problems subject to nonlinear PDE constraints based on the occupation measure formalism. The m…
A closed-measure approach to stochastic approximation
Pascal Bianchi, Rodolfo Rios-Zertuche
This paper introduces a new method to tackle the issue of the almost sure convergence of stochastic approximation algorithms defined from a differential inclusion. Under the assump…
Examples of pathological dynamics of the subgradient method for Lipschitz path-differentiable functions
Rodolfo Rios-Zertuche
We show that the vanishing stepsize subgradient method -- widely adopted for machine learning applications -- can display rather messy behavior even in the presence of favorable as…
Long term dynamics of the subgradient method for Lipschitz path differentiable functions
Jerome Bolte, Edouard Pauwels, Rodolfo Rios-Zertuche
We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function i…
Weak KAM theory in higher-dimensional holonomic measure flows
Rodolfo Rios-Zertuche
We construct a weak KAM theory for parameterized cobordisms and their relaxation, holonomic measures. We find a weak kam solution in that context, and we show that in many cases it…
Deformations of closed measures and variational characterization of measures invariant under the Euler-Lagrange flow
Rodolfo Rios-Zertuche
The set of closed (or holonomic) measures provides a useful setting for studying optimization problems because it contains all curves, while also enjoying good compactness and conv…
Existence of differentiable curves in convex sets and the concept of direction of the flow in mass transportation
Rodolfo Rios-Zertuche
In this paper we consider convex subsets of locally-convex topological vector spaces. Given a fixed point in such a convex subset, we show that there exists a curve completely cont…
Characterization of minimizable Lagrangian action functionals and a dual Mather theorem
Rodolfo Rios-Zertuche
We show that a necessary and sufficient condition for a smooth function on the tangent bundle of a manifold to be a Lagrangian density whose action can be minimized is, roughly spe…
Polygonal approximations of closed parametric varifolds
Rodolfo Rios-Zertuche
We define holonomic measures to be certain analogues of varifolds that keep track of the local parameterization and orientation of the submanifold they represent. They are Borel me…
The variational structure of the space of holonomic measures
Rodolfo Rios-Zertuche
Roughly speaking, holonomic measures are parametric varifolds without boundary. They provide a setting appropriate for the analysis of many variational problems. In this paper, we…
Distributions that arise as derivatives of families of measures
Rodolfo Rios-Zertuche
We characterize the distributions that arise as derivatives of families of probabilities and of positive and signed measures on smooth manifolds.
An introduction to the half-infinite wedge
Rodolfo Rios-Zertuche
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of th…
The Pillowcase Distribution and Near-Involutions
Rodolfo Rios-Zertuche
In the context of the Eskin-Okounkov approach to the calculation of the volumes of the different strata of the moduli space of quadratic differentials, the important ingredients ar…
Near-Involutions, the Pillowcase Distribution, and Quadratic Differentials
Rodolfo Rios-Zertuche
In the context of A. Eskin and A. Okounkov's approach to the calculation of the volumes of the different strata of the moduli space of quadratic differentials, two objects have a p…