Displaying similar documents to “Hamiltonian trajectories and saddle points in mathematical economics”

Smooth optimal synthesis for infinite horizon variational problems

Andrei A. Agrachev, Francesca C. Chittaro (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification...

Arrow-type sufficient conditions for optimality of age-structured control problems

Vladimir Krastev (2013)

Open Mathematics

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We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).

Symplectic Pontryagin approximations for optimal design

Jesper Carlsson, Mattias Sandberg, Anders Szepessy (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the hamiltonian; next the solution to its stationary hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the hamiltonian function...