Second order Hamilton–Jacobi–Bellman inequalities
Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 591-596.

This work is devoted to the study of a class of Hamilton–Jacobi–Bellman inequalities which come from an optimal control problem where the state equation is a stochastic variational inequality. We show that the value function, which minimizes the cost, is a viscosity solution of the studied equation. This approach is made by perturbing the initial problem. Then we prove the uniqueness of the inequality.

Cette note est consacrée à l'étude des inéquations aux dérivées partielles du type Hamilton–Jacobi–Bellman issues d'un problème de contrôle optimal où l'équation d'état est une inéquation variationnelle stochastique. En fait, on démontre que la fonction minimisant la fonctionnelle de coût est une solution de viscosité pour l'équation étudiée. Cette approche est menée par une méthode de perturbation du problème initial. L'unicité de la solution de viscosité est également prouvée.

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DOI: 10.1016/S1631-073X(02)02528-1
Zălinescu, Adrian 1

1 Université de Bretagne Occidentale, 6, avenue Victor le Gorgeu, BP 809, 29285 Brest cedex, France
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Zălinescu, Adrian. Second order Hamilton–Jacobi–Bellman inequalities. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 591-596. doi : 10.1016/S1631-073X(02)02528-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02528-1/

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