On the worst scenario method: Application to uncertain nonlinear differential equations with numerical examples
On Theoretical and Numerical Aspects of the Bang-Bang-Principle.
On Tridiagonal Linear Complementary Problems.
Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization.
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...
Optimal Control of a Stefan Problem with State-Space Constraints.
Optimal control of dynamical processes in two-phase systems of solid-liquid type
Optimal control of fluid flow in soil 1. Deterministic case.
We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation...
Optimal control of the Primitive Equations of the ocean with Lagrangian observations
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
Optimal control of the time-varying flows in networks
Optimal Cycles in Doubly Weighted Graphs and Approximation of Bivariate Functions by Univariate Ones.
Optimal design in small amplitude homogenization
This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide...
Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem
A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...
Optimal discrete approximation of continuous linear operators applicable to control problems
Optimal multiphase transportation with prescribed momentum
A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.
Optimal Multiphase Transportation with prescribed momentum
A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.
Optimal traffic assignment in a SS/TDMA frame : a new approach by set covering and column generation
Optimisation connexe en dimension finie par relaxation
Optimisation de procédés chimiques par une méthode de gradient réduit. Partie II. Exemples d'illustration. Comparaison avec d'autres méthodes