Rabah Tahraoui

On the strict concavity of the harmonic radius in dimension N>=3

Abstract In this paper a result on the strict concavity of the harmonic radius in open convex domains of R N , for N⩾3, is given. It implies the strict convexity of the Robin function and the uniqueness of the harmonic center in bounded convex domains.

Maximum principle for elliptic operators and applications

Abstract Let f be a signed function defined on some bounded domain Ω . We give sufficient conditions ensuring the positivity of u, solution of the following equation: −Δu=f in Ω, u| ∂Ω =0.

Production planning and inventories optimization with a general storage cost function

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 whereas the cost of storage has no particular properties of convexity. First, in spite of this non-convexity, we give an existence result. Second, from the necessary conditions, we derive some precise qualitative description of the optimal plan. In particular, we obtain that inventory accumulation is not optimal.

Optimal control in elliptic equations

The goal of this work is to study problems of control when the state is governed by an elliptic partial differential equation. The control dependency is nonconvex. These kinds of problems arise in such applications as domain control or hydrodynamics. Examples are provided.

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.

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.