Algorithms for general mixed quasi variational inequalities.
Allard type regularity results for varifolds with free boundaries
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
Almost continuous solutions of geometric Hamilton–Jacobi equations
Almost Every Curve in R3 Bounds a Unique Area Minimizing Surface.
Almost metric versions of Zhong's variational principle
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.
Alternating Iteration and Elliptic Variational Inequalities.
Alternative polynomial equation approach to LQ discrete-time open-loop control
Alternative polynomial equation approach to LQ discrete-time feedback control
A-monotone nonlinear relaxed cocoercive variational inclusions
Based on the notion of A - monotonicity, a new class of nonlinear variational inclusion problems is presented. Since A - monotonicity generalizes H - monotonicity (and in turn, generalizes maximal monotonicity), results thus obtained, are general in nature.
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a priori Campanato type regularity condition for local minimisers in the calculus of variations
An a priori Campanato type regularity condition is established for a class of W1X local minimisers of the general variational integral where is an open bounded domain, F is of class C2, F is strongly quasi-convex and satisfies the growth condition for a p > 1 and where the corresponding Banach spaces X are the Morrey-Campanato space , µ < n, Campanato space and the space of bounded mean oscillation . The admissible maps are of Sobolev class W1,p, satisfying a Dirichlet boundary...
An a Priori Estimate for the Oscillation of the Normal to a Hypersurface Whose First and Second Variation With Respect to an Elliptic Integrand is Controlled.
An abstract differential inequality and eigenvalues of variational inequalities
An abstract setting for differential Riccati equations in optimal control problems for hyperbolic/Petrowski-type P. D. E. s with boundary control and slightly smoothing observation.
An active set strategy based on the augmented lagrangian formulation for image restoration
An active set strategy based on the augmented Lagrangian formulation for image restoration
Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...
An algebraic characterization of quasi-Möbius homeomorphisms. (Une caractérisation algébrique des homéomorphismes quasi-Möbius.)