We study the limit behavior of certain classes of dependent random sequences (processes) which do not possess the Markov property. Assuming these processes depend on a control parameter we show that the optimization of the control can be reduced to a problem of nonlinear optimization. Under certain hypotheses we establish the stability of such optimization problems.
In der Arbeit geht es um die Charakteristik des allgemeinen Begriffs der asymptotischen Berührung von solchen abgeschlossenen, konvexen Mengen in , wo ihr Abstand gleich Null und ihr Durchschnitt leer ist. Es wird gezeigt, dass unter diesem Umstand man dem fraglichen Mengenpaar ein Tripel von natürlichen Zahlen (die Ordnung der Berührung, der Grad der Berührung und die Diemnsion des zugehörigen asymptotischen, linearen Raumes), welches eine Charakteristik dieser Berührung darstellt, eindeutig zuordnen...
In this paper, the augmented Lagrangian method is investigated for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The objective function of stochastic linear programming problem is piecewise linear and non-differentiable. Therefore, to use a smooth optimization methods, the objective function is approximated by a differentiable and piecewise quadratic function. Using quadratic approximation, it is required to obtain the...
We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through a closed formula. A full convergence analysis is provided, allowing for inexact solution of the subproblems. ...
Data collected by statistical offices generally contain errors, which have to be corrected before reliable data can be published. This correction process is referred to as statistical data editing. At statistical offices, certain rules, so-called edits, are often used during the editing process to determine whether a record is consistent or not. Inconsistent records are considered to contain errors, while consistent records are considered error-free. In this article we focus on automatic error localisation...
Cet article est la suite de l’article «Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : formalisme unifié et classes d’approximation» où nous avons présenté et discuté, dans le cadre d’un nouveau formalisme pour l’approximation polynomiale (algorithmique polynomiale à garanties de performances pour des problèmes NP-difficiles), des outils permettant d’évaluer, dans l’absolu, les proporiétés d’approximation de problèmes difficiles. Afin de répondre pleinement à l’objectif...
This paper is the continuation of the paper “Autour de nouvelles notions pour l'analyse des algorithmes d'approximation: Formalisme unifié et classes d'approximation” where a new formalism for polynomial approximation and its basic tools allowing an “absolute” (individual) evaluation the approximability properties of NP-hard problems have been presented and discussed. In order to be used for exhibiting a structure for the class NPO (the optimization problems of NP), these tools must be enriched...
This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.
This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.