Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality
Error estimates for finite element approximations of elliptic control problems
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....
Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states. ...
Finite difference approximation of control via the potential in a 1-D Schrödinger equation.
Finite element error analysis for state-constrained optimal control of the Stokes equations
Finite-difference approximation of energies in fracture mechanics
Finite-differences discretizations of the Mumford-Shah functional
Finite-differences discretizations of the mumford-shah functional
About two years ago, Gobbino [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals. In this work, we introduce a discretized version of De Giorgi's approximation, that may be seen as a generalization of Blake and Zisserman's “weak membrane” energy (first introduced in the image segmentation framework). A simple adaptation of Gobbino's results allows us to compute the Γ-limit of this discrete functional...
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators
Image Compression with Schauder Bases
As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...
-error analysis for a system of quasivariational inequalities with noncoercive operators.
Linear convergence in the approximation of rank-one convex envelopes
A linearly convergent iterative algorithm that approximates the rank-1 convex envelope of a given function , i.e. the largest function below which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.
Linear convergence in the approximation of rank-one convex envelopes
A linearly convergent iterative algorithm that approximates the rank-1 convex envelope of a given function , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.
Linear programming interpretations of Mather’s variational principle
We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
Linear programming interpretations of Mather's variational principle
We discuss some implications of linear programming for Mather theory [13-15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [5-8].
Méthode de décomposition pour un problème unilatéral de type parabole
Minimax optimal control problems. Numerical analysis of the finite horizon case