A Canonical Formalism for Multiple Integral Problems in the Calculus of Variation. (Short Communication).
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Hanno Rund (1968)
Aequationes mathematicae
A. Adamski, A. Korytowski, W. Mitkowski (1977)
Applicationes Mathematicae
J. Frédéric Bonnans, Élisabeth Ottenwaelter, Housnaa Zidani (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani, SIAM J. Numer. Anal. 41 (2003) 1008–1021]. The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in operations, where is the size of the stencil....
J. Frédéric Bonnans, Élisabeth Ottenwaelter, Housnaa Zidani (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in [Bonnans and Zidani, SIAM J. Numer. Anal.41 (2003) 1008–1021]. The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in O(pmax) operations, where pmax is the size of...
S.P. LIPSHITZ (1971)
Aequationes mathematicae
S.P. LIPSHITZ (1971)
Aequationes mathematicae
Otton Martin Nikodym (1971)
Journal für die reine und angewandte Mathematik
Heinz Schättler, Miroslava Jankovic (1993)
Forum mathematicum
F. Pelletier, L. Bouche (1995)
Banach Center Publications
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
G. Barles (1990)
Annales de l'I.H.P. Analyse non linéaire
Moritz Armsen (1975)
Aequationes mathematicae
Piermarco Cannarsa, Giuseppe Da Prato (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
Moritz Armsen (1976)
Aequationes mathematicae
G. V. Rao (1972)
RAIRO - Operations Research - Recherche Opérationnelle
Vilém Novák (1976)
Kybernetika
Hanno Rund (1975)
Aequationes mathematicae
Hanno Rund (1975)
Aequationes mathematicae
Vieri Benci, Paul H. Rabinowitz (1979)
Inventiones mathematicae
Philip D. Loewen, Frank H. Clarke, Richard B. Vinter (1988)
Annales de l'I.H.P. Analyse non linéaire
Ivar Ekeland (1977)
Publications Mathématiques de l'IHÉS
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