Noticias en español
Extragradient method with variance reduction for pseudo-monotone stochastic variational inequalities
Resumen: We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set, unbounded operator, non-uniform variance of the oracle and, also, we do not require any regularization. Alongside the stochastic approximation procedure, we iteratively reduce the variance of the stochastic error. Our method attains the optimal oracle complexity O(1/epsilon^2) (up to a logarithmic term) and an accelerated rate O(1/K) in terms of the...
Read MoreConvex Nonlinear Relaxations of the Pooling Problem
Resumen: We investigate relaxations for the non-convex pooling problem, which arises in production planning problems in which products with are mixed in intermediate “pools” in order to meet quality targets at their destinations. We derive valid nonlinear convex inequalities, which we conjecture define the convex hull of this continuous non-convex set for some special cases. Numerical illustrations of the results will be presented.
Read MoreBe-CoDiS: A mathematical model to predict the risk of human diseases spread between countries. Validation and application to the 2014-15 Ebola Virus Disease epidemic
RESUMEN: Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the United Kingdom, the USA and Spain. Regarding the emergency of this situation, there is a need of development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Be-CoDiS (Between-Countries...
Read MoreEquivalence between the p-cyclic quasimonotonicity and the p-cyclic monotonicity for affine maps.
Resumen: It is well known that, for general multivalued operators, monotonicity implies quasimonotonicity. This is also true if we deal with cyclic monotone/quasimonotone or even p-cyclic monotone/quasimonotone operators. In this work, we prove, in general Banach spaces, that an affine p-cyclic quasimonotone operator is in fact p-cyclic monotone.
Read MoreAbout Moreau-Yosida regularization of the minimal time crisis problem.
Resumen: We study an optimal control problem where the cost functional to be minimized represents the so-called time of crisis, i.e. the time spent by a trajectory solution of a control system outside a given set K. This functional can be expressed using the indicator of K, that is discontinuous preventing the use of the standard Maximum Principle. We consider a regularization scheme of the problem based on the Moreau-Yosida approximation of the characteristic function of K. We prove the convergence of an optimal sequence for the approximated problem to an optimal solution of the original...
Read MoreA CHARACTERIZATION OF THE RADON-NIKODYM PROPERTY. APPLICATION TO THE CONSTRUCTION OF ALMOST CLASSICAL SOLUTIONS OF HAMILTON-JACOBI EQUATIONS.
Resumen: We prove that a Banach space X has the Radon-Nikodym property if and only if a certain perturbed minimization principle holds. We apply this result to the construction of everywhere differentiable functions which are solution almost everywhere of some Hamilton-Jacobi equation.
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