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Approximation of maximal Cheeger sets by projection

Guillaume Carlier, Myriam Comte, Gabriel Peyré (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of ℝ d . This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to compute maximal Cheeger sets and Cheeger constants.

Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels

Alexis Guigue (2014)

ESAIM: Control, Optimisation and Calculus of Variations

This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...

Approximation of the Snell envelope and american options prices in dimension one

Vlad Bally, Bruno Saussereau (2002)

ESAIM: Probability and Statistics

We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

Approximation of the Snell Envelope and American Options Prices in dimension one

Vlad Bally, Bruno Saussereau (2010)

ESAIM: Probability and Statistics

We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Jakub Kůdela, Pavel Popela (2018)

Kybernetika

In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....

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