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Augmented Lagrangian method for recourse problem of two-stage stochastic linear programming

Saeed Ketabchi, Malihe Behboodi-Kahoo (2013)

Kybernetika

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...

Augmented Lagrangian methods for variational inequality problems

Alfredo N. Iusem, Mostafa Nasri (2010)

RAIRO - Operations Research

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. ...

Automatic error localisation for categorical, continuous and integer data.

Ton de Waal (2005)

SORT

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...

Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : de la structure de NPO à la structure des instances

Marc Demange, Vangelis Paschos (2002)

RAIRO - Operations Research - Recherche Opérationnelle

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...

Autour de nouvelles notions pour l'analyse des algorithmes d'approximation : de la structure de NPO à la structure des instances

Marc Demange, Vangelis Paschos (2010)

RAIRO - Operations Research

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...

Average cost Markov control processes with weighted norms: existence of canonical policies

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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.

Average cost Markov control processes with weighted norms: value iteration

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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.

Balanced problems on graphs with categorization of edges

Štefan Berežný, Vladimír Lacko (2003)

Discussiones Mathematicae Graph Theory

Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: L ( D ) = m a x 1 i p ( m a x e S i D w ( e ) - m i n e S i D w ( e ) ) For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary...

Balancing the stations of a self service “bike hire” system

Mike Benchimol, Pascal Benchimol, Benoît Chappert, Arnaud de la Taille, Fabien Laroche, Frédéric Meunier, Ludovic Robinet (2011)

RAIRO - Operations Research

This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that v V x v = v V y v and all quantities...

Balancing the stations of a self service “bike hire” system

Mike Benchimol, Pascal Benchimol, Benoît Chappert, Arnaud de la Taille, Fabien Laroche, Frédéric Meunier, Ludovic Robinet (2011)

RAIRO - Operations Research

This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that v V x v = v V y v and all quantities...

Batch scheduling problem with due-date and fuzzy precedence relation

Xuesong Li, Hiroaki Ishii, Minghao Chen (2012)

Kybernetika

A single-machine batch scheduling problem is investigated. Each job has a positive processing time and due-date. Setup times are assumed to be identical for all batches. All batch sizes cannot exceed a common upper bound. As in many practical situations, jobs have to be subject to flexible precedence constraints. The aim of this paper is to find an optimal batch sequence. The sequence is to minimize the maximal completion time and maximize the minimum value of desirability of the fuzzy precedence....

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