An existence theorem for set differential inclusions in a semilinear metric space
An optimal control problem for an elliptic variational inequality
Approximation methods for nonlinear problems with constraints in form of variational inequalities
Approximations by regular sets and Wiener solutions in metric spaces
Let be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for -harmonic functions and to show that they coincide with three other notions of generalized solutions.
Characterizations of p-superharmonic functions on metric spaces
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...
Commandes généralisées à valeurs dans un espace compact théorèmes d'existence
Common solutions of an iterative scheme for variational inclusions, equilibrium problems, and fixed point problems.
Conservation Criteria, Canonical Transformations, and Integral Invariants in the Field Theory of Carathéodory for Multiple Integral Variational Problems. (Short Communication).
Conservation criteria, canonical transformations, and integral invariants in the field theory of Carathéodory for multiple integral variational problems.
Constrained optimal control. The algebraic approach
Constrained optimization: A general tolerance approach
To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....
Contrôle de min-max et feedback linéaire pour des systèmes dynamiques approchés en norme
Convergence d'un schéma de minimisation alternée
Convergence uniforme pour les itérés définissant la solution d'une inéquation quasi-variationnelle
Critical Point Theorems for Indefinite Functionals.
Duality in vector optimization. I. Abstract duality scheme
Enlarged Asymptotic Compensation in Discrete Distributed Systems
This work concerns an enlarged analysis of the problem of asymptotic compensation for a class of discrete linear distributed systems. We study the possibility of asymptotic compensation of a disturbance by bringing asymptotically the observation in a given tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the unicity of the optimal control ensuring this compensation and we give its characterization
Enlarged exact compensation in distributed systems
In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study...
Equivalent formulation and numerical analysis of a fire confinement problem
We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂. In this paper we show that the search for blocking strategies...
Evolutionary variational inequalities and applications in plasticity
An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.