Displaying similar documents to “Convergence of gradient-based algorithms for the Hartree-Fock equations”

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large- result of [M. Griesemer and F. Hantsch, (2011) 170]. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient...

Computing and proving with pivots

Frédéric Meunier (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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A simple idea used in many combinatorial algorithms is the idea of . Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset to a new one ′ by deleting an element inside and adding an element outside : ′ =  ...

Dimension reduction for −Δ1

Maria Emilia Amendola, Giuliano Gargiulo, Elvira Zappale (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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A 3D-2D dimension reduction for −Δ is obtained. A power law approximation from −Δ as  → 1 in terms of -convergence, duality and asymptotics for least gradient functions has also been provided.

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....

Analysis of a near-metric TSP approximation algorithm

Sacha Krug (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the -metric traveling salesman problem ( -TSP), , the TSP restricted to graphs satisfying the -triangle inequality ({}) ≤ (({}) + ({})), for some cost function and any three vertices . The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3 /2 and is the best known algorithm for the -TSP, for 1 ≤  ≤ 2....

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We study integral functionals constrained to divergence-free vector fields in on a thin domain, under standard -growth and coercivity assumptions, 1    ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject...

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in -norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate information of smoothness/sparsity on the inhomogeneity...

Extension of Reverse Elimination Method Through a Dynamic Management of the Tabu List

Saïd Hanafi, Arnaud Fréville (2010)

RAIRO - Operations Research

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The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called REM-...

Differential approximation of NP-hard problems with equal size feasible solutions

Jérôme Monnot (2010)

RAIRO - Operations Research

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In this paper, we focus on some specific optimization problems from graph theory, those for which all feasible solutions have an equal size that depends on the instance size. Once having provided a formal definition of this class of problems, we try to extract some of its basic properties; most of these are deduced from the equivalence, under differential approximation, between two versions of a problem  which only differ on a linear transformation of their objective functions. This...

Inequality-sum: a global constraint capturing the objective function

Jean-Charles Régin, Michel Rueher (2010)

RAIRO - Operations Research

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This paper introduces a new method to prune the domains of the variables in constrained optimization problems where the objective function is defined by a sum , and where the integer variables are subject to difference constraints of the form . An important application area where such problems occur is deterministic scheduling with the as optimality criteria. This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical...

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Francis Filbet, Amélie Rambaud (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet and S. Jin [229 (2010)] and G. Dimarco and L. Pareschi [49 (2011) 2057–2077] in the context of nonlinear and stiff kinetic equations. Here, we propose a convergence analysis of such a scheme for the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation law. We investigate the convergence of the approximate solution ( ...

A note on a two dimensional knapsack problem with unloading constraints

Jefferson Luiz Moisés da Silveira, Eduardo Candido Xavier, Flávio Keidi Miyazawa (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper we address the two-dimensional knapsack problem with unloading constraints: we have a bin , and a list of rectangular items, each item with a class value in {1,...,}. The problem is to pack a subset of into , maximizing the total profit of packed items, where the packing must satisfy the unloading constraint: while removing one item , items with higher class values can not block . We present a (4 + )-approximation algorithm when the bin is a square. We also present (3 + )-approximation...

New algorithms for coupled tasks scheduling – a survey

Jacek Blazewicz, Grzegorz Pawlak, Michal Tanas, Wojciech Wojciechowicz (2012)

RAIRO - Operations Research - Recherche Opérationnelle

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The coupled tasks scheduling problem is a class of scheduling problems introduced for beam steering software of sophisticated radar devices, called phased arrays. Due to increasing popularity of such radars, the importance of coupled tasks scheduling is constantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, and only a few practically usable algorithms for such problems were found. This paper provides a survey of already known complexity results of various...

Solving multi-agent scheduling problems on parallel machines with a global objective function

F. Sadi, A. Soukhal, J.-C. Billaut (2014)

RAIRO - Operations Research - Recherche Opérationnelle

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In this study, we consider a scheduling environment with ( ≥ 1) parallel machines. The set of jobs to schedule is divided into disjoint subsets. Each subset of jobs is associated with one agent. The agents compete to perform their jobs on common resources. The objective is to find a schedule that minimizes a global objective function , while maintaining the regular objective function of each agent, , at a level no greater than a fixed value, ...

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study integral functionals constrained to divergence-free vector fields in on a thin domain, under standard -growth and coercivity assumptions, 1    ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject...

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( =   < 1), or is much greater than ( =   > 1). We consider all three cases. ...