Stochastische dynamische Optimierung als Spezialfall linearer Optimierung in halbgeordneten Vektorräumen.
Sub-riemannian sphere in Martinet flat case
Sub-Riemannian sphere in Martinet flat case
This article deals with the local sub-Riemannian geometry on ℜ3, (D,g) where D is the distribution ker ω, ω being the Martinet one-form : dz - ½y2dxand g is a Riemannian metric on D. We prove that we can take g as a sum of squares adx2 + cd2. Then we analyze the flat case where a = c = 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence...
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems.
Symplectic Pontryagin approximations for optimal design
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 can be...
Symplectic Pontryagin approximations for optimal design
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...
Systèmes dynamiques et fibrations. Concept d'opt-automate