27 research outputs found
On some systems controlled by the structure of their memory
We consider an optimal control problem governed by an ODE with memory playing
the role of a control. We show the existence of an optimal solution and derive
some necessary optimality conditions. Some examples are then discussed
Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory
This article is devoted to the optimal control of state equations with memory
of the form: ?[x(t) = F(x(t),u(t), \int_0^{+\infty} A(s) x(t-s) ds), t>0, with
initial conditions x(0)=x, x(-s)=z(s), s>0.]Denoting by the
solution of the previous Cauchy problem and: where is a
class of admissible controls, we prove that is the only viscosity solution
of an Hamilton-Jacobi-Bellman equation of the form: in the sense of the
theory of viscosity solutions in infinite-dimensions of M. Crandall and P.-L.
Lions
Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric
We study a second-order variational problem on the group of diffeomorphisms
of the interval [0, 1] endowed with a right-invariant Sobolev metric of order
2, which consists in the minimization of the acceleration. We compute the
relaxation of the problem which involves the so-called Fisher-Rao functional a
convex functional on the space of measures. This relaxation enables the
derivation of several optimality conditions and, in particular, a sufficient
condition which guarantees that a given path of the initial problem is also a
minimizer of the relaxed one. This sufficient condition is related to the
existence of a solution to a Riccati equation involving the path acceleration.Comment: 34 pages, comments welcom
Production Planning and Inventories Optimization: A Backward Approach in the Convex Storage Cost Case
As in [3], we study the deterministic optimization problem of a profit-maximizing firm which plans its sales/production schedule. The firm knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. Here, we also assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of an integro-di_erential backward equation, from which we obtainan explicit construction of the optimal plan.Production planning, inventory management, integro-dfferential backwardequations.
Production Planning and Inventories Optimization: A Backward Approach in the Convex Storage Cost Case.
We study the deterministic optimization problem of a profit-maximizing firm which plans its sales/production schedule. The firm controls both its production and sales rates and knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. In Chazal et al. [Chazal, M., Jouini, E., Tahraoui, R., 2003. Production planning and inventories optimization with a general storage cost function. Nonlinear Analysis 54, 1365–1395], we provide an existence result and derive some necessary conditions of optimality. Here, we further assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of a backward integro-differential equation, from which we obtain an explicit construction of the optimal plan.Production Planning; Inventory Management; Integro-differential Equations;
Production Planning and Inventories Optimization : A Backward Approach in the Convex Storage Cost Case
As in [1], we study the deterministic optimization problem of a profit- maximizing firm which plans its sales/production schedule. The firm knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. Here, we also assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of an integro-differential backward equation, from which we obtain an explicit construction of the optimal plan.Production planning, inventory management, integro- differential backward equations