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  • Strömberg, Ann-Brith, 1961-, et al. (författare)
  • Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
  • 2020
  • Ingår i: Numerical Nonsmooth Optimization. - 978-3-030-34910-3 ; s. 499-547
  • Bokkapitel (övrigt vetenskapligt)abstract
    • This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
  • Wang, Siyang, et al. (författare)
  • 2018
  • Ingår i: Mathematics of Computation. - 0025-5718. ; 87:314, s. 2737-2763
  • Tidskriftsartikel (refereegranskat)abstract
    • When using a finite difference method to solve an initial-boundaryvalue problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
  • Fotedar, Sunney, 1989-, et al. (författare)
  • Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
  • 2019
  • Ingår i: Taktisk resursallokering för effektivt kapacitetsutnyttjande.
  • Konferensbidrag (refereegranskat)abstract
    • In the aerospace industry, with low volumes and many products, there is a critical need to efficiently use available manufacturing resources. Currently, at GKN Aerospace, resource allocation decisions that in many cases will last for several years are to some extent made with a short-term focus so as to minimize machining time, which results in a too high load on the most capable machines, and too low load on the less capable ones. This creates an imbalance in capacity utilization that leads to unnecessary queuing at some machines, resulting in long lead times and in an increase in tied-up capital. Tactical resource allocation on the medium to long-range planning horizon (six months to several years) aims to address this issue by allocating resources to meet the predicted future demand as effectively as possible, in order to ensure long range profitability. Our intent is to use mathematical optimization to find the best possible allocations.
  • Gerlee, Philip, 1980-, et al. (författare)
  • Scientific Models Red Atoms, White Lies and Black Boxes in a Yellow Book
  • 2016
  • Bok (övrigt vetenskapligt)abstract
    • A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields.The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
  • Vasilis, Jonatan, 1981- (författare)
  • Harmonic measures
  • 2010
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel.Fix a domain and a boundary point, subject to certain regularity conditions. Consider the part of the boundary that lies within a disc, centered at the fixed boundary point. It is shown that as the radius of the disc tends to zero, the p-harmonic measure of the boundary set decays as an explicitly given power of the radius.The square root of the Poisson kernel is studied in both continuous and discrete settings. In the continuous case the domain is the unit disc, and a Hardy space related to the square root of the Poisson kernel is defined. The main result is that, as opposed to the classical Hardy space, the positive functions do not admit a characterization in terms of an Orlicz space. Similar results are given also in the discrete case, where the domain is instead a regular tree.Further results in the discrete setting include the construction of a nearest neighbor random walk on the tree with exit distribution determined by powers of the Poisson kernel. The minimally thin sets of these random walks are characterized.Finally, we suggest a generalization of a two-dimensional geometric result – the ring lemma – to three dimensions.
  • Hamon, Thierry, et al. (författare)
  • Term Ranking Adaptation to the Domain : Genetic Algorithm-Based Optimisation of the C-Value
  • 2014
  • Ingår i: Advances in Natural Language Processing : 9th International Conference on NLP, PolTAL 2014, Warsaw, Poland, September 17-19, 2014. Proceedings. - Springer International Publishing. - 978-3-319-10888-9 ; s. 71-83
  • Konferensbidrag (refereegranskat)abstract
    • <p>Term extraction methods based on linguistic rules have been proposed to help the terminology building from corpora. As they face the difficulty of identifying the relevant terms among the noun phrases extracted, statistical measures have been proposed. However, the term selection results may depend on corpus and strong assumptions reflecting specific terminological practice. We tackle this problem by proposing a parametrised <em>C-Value</em> which optimally considers the length and the syntactic roles of the nested terms thanks to a genetic algorithm. We compare its impact on the ranking of terms extracted from three corpora. Results show average precision increased by 9% above the frequency-based ranking and by 12% above the <em>C-Value</em>-based ranking.</p>
  • Jagers, Peter, 1941- (författare)
  • Matematikens ord
  • 2009
  • Ingår i: LexicoNordica. ; 16, s. 315-318
  • Tidskriftsartikel (refereegranskat)
  • Pejlare, Johanna, 1976-, et al. (författare)
  • On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements
  • 2016
  • Ingår i: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2-909916-51-0 ; s. 513-523
  • Konferensbidrag (refereegranskat)abstract
    • In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
  • Pejlare, Johanna, 1976- (författare)
  • On the relationships between the geometric and the algebraic ideas in Duhre’s textbooks of mathematics, as reflected via Book II of Euclid’s Elements
  • 2017
  • Ingår i: “DIG WHERE YOU STAND” 4. Proceedings of the Fourth International Conference on the History of Mathematics Education. 23-26 September, 2015. Torino, Italy. - Roma : Edizioni Nuova Cultura. - 9788868128647
  • Konferensbidrag (refereegranskat)abstract
    • The present article explores the relationships between the geometric and algebraic ideas presented in Anders Gabriel Duhre’s mathematics textbooks. Of particular interest is Book II of Euclid’s Elements as presented by Duhre in his textbook on geometry from 1721. We consider in detail Duhre’s two versions of Proposition II.5, dealing with straight lines cut into equal and unequal parts, as well as the two proofs of the propositions that he presents. Duhre’s formulations are slightly different from traditional geometric formulations, as he moved away from a purely geometrical context towards an algebraic one. Duhre established Proposition II.5 using algebra in Descartes’ notation as well as in the notation of Wallis and Oughtred. Duhre ́s reason for introducing algebra in Book II of Euclid’s Elements was to obtain convenience in calculations, as well as the possibility to generalize results to different kinds of quantities.
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