In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a contro...

In this paper we present a method for determining some variations of a singular trajectory of an affine control system. These variations provide necessary optimality conditions which may distinguish between maximizing and minimizing problems. The generalized Legendre-Clebsch conditions are an example of these type of conditions.

Abstract: We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to nonconvex stochastic optimization problems with stochastic dominance constraints, ge...

We consider the problem of routing uniform communication instances in switched optical tori that use the wavelength division multi-plexing (or WDM) approach. A communication instance is called uniform if it consists exactly of all pairs of nodes in the graph whose distance is equal to one from a speciied set S = fd1; d2; : : : ; d k g. We give bounds on the optimal load induced on an edge for a...

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V eronique Maume-Deschamps Section de Math ematiques, Universit e de Gen eve 2-4 rue du Lievre CP 240 Suisse. Abstract Let T be a measurable map on a Polish space X, let Y be a non trivial subset of X. We give conditions ensuring existence of conditionally invariant probability measures (to non absorption in Y). We also supply suucient conditions for these probability measures to be absolutely ...

The aim of this note is to present the necessary optimality conditions for a model (in closed population) of an immunizing disease similar to hepatitis B following. We study the impact of medical tests and controls involved in curing this kind of immunizing disease and deduced a well posed adjoint system if there exists an optimal control.

In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a longtime smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is c...

It has been observed empirically that a simple linearization method applied to the problem of finding maximal solutions to systems of linear inequalities frequently terminates in one step. This is normally a Kuhn-Tucker point, and depending on the starting point, can be a global solution. An explanation of this phenomenon is given, and this is illustrated by examples.