A Canonical Formalism for Multiple Integral Problems in the Calculus of Variation. (Short Communication).
A conception of optimality for algorithms and its application to the optimal search for a minimum
A fast algorithm for the two dimensional HJB equation of stochastic control
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....
A fast algorithm for the two dimensional HJB equation of stochastic control
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...
A Solution of the 'Converse Canonical Problem' for Multiple Integrals in the Calculus of Variations (Short Communication)
A Solution of the 'Converse Canonical Problem' for Multiple Integrals in the Calculus of Variations
A study in the Lagranges variational problem considered in the large.
A synthesis of time-optimal controls in the presence of saturated singular arcs.
Abnormality of trajectory in sub-Riemannian structure
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...
An approach of deterministic control problems with unbounded data
An Embedding Theorem in the Calculus of Variations for Multiple Integrals.
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
An imbedding theorem in the calculus of variations for multiple integrals, addendum.
An optimal decision procedure using dynamic programming technique
Complex system evaluating function
Conservation Criteria, Canonical Transformations, and Integral Invariants in the Field Theory of Carathéodory for Multiple Integral Variational Problems. (Short Communication).
Conservation criteria, canonical transformations, and integral invariants in the field theory of Carathéodory for multiple integral variational problems.
Critical Point Theorems for Indefinite Functionals.
Differential inclusions with free time
Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations