In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality const...

A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite-dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short-step path-following method is established.

In this work, methods to detect one or several change points in multivariate time series are reviewed. They include retrospective (o -line) procedure such as maximum likelihood estimation, regression, kernel methods, etc. In this large area of research, applications are numerous and diverse; many di erent models and operational constraints (on precision, complexity,...) exist. A formal framewor...

Recently, adaptive wavelet stratégies for symmetrie, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetrie, but indefinite. Firstly, we investigate a posteriori error estimâtes and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this ...

Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their lowdegree polynomial worst-case complexity ...

Projected Krylov methods are full-space formulations of Krylov methods that take place in a nullspace. Provided projections into the nullspace can be computed accurately, those methods only require products between an operator and vectors lying in the nullspace. We provide systematic principles for obtaining the projected form of any well-defined Krylov method. Projected Krylov methods are math...

An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is splitted into the sum of a single-valued operator F , possessing a kind of pseudo Dunn property, and a maximal monotone operator Q. The current auxiliary problem is constructed by fixing F at the...

In this paper we use interior-point methods for linear programming, developed in t,he contest of sequential computation, to obtain a parallel algorithm for t,he bipartite matching problem. Our algorithm runs in 0*(,/E) time I. Our results extend to the weighted bipartite matching problem and to the zero-one minimum-cost flow problem, yielding O*( filog C’) algorithms?. This improvk’previous bou...

Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow probl...

In this paper we present a selection of fixed point theorems with applications in nonlinear analysis. We begin with the Banach fixed point theorem, which we use to prove the inverse and implicit mapping theorems and the Picard-Lindelöf theorem for Banach spaces. We then prove in succession the fixed point theorems of Brouwer, Schauder, and Schaeffer, after which we conclude with two example app...