Готові списки джерел за темами / Polyhedral approaches

Добірка наукової літератури з теми "Polyhedral approaches"

Автор: Grafiati

Опубліковано: 21 липня 2022

Оновлено: 8 серпня 2022

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Статті в журналах з теми "Polyhedral approaches":

Feng, Y. T., and Yuanqiang Tan. "On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra." Engineering Computations 37, no. 1 (August 12, 2019): 54–72. http://dx.doi.org/10.1108/ec-03-2019-0124.

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Purpose Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking. Design/methodology/approach In this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted. Findings Numerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small. Originality/value The equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.

Fercoq, Olivier, Marianne Akian, Mustapha Bouhtou, and Stephane Gaubert. "Ergodic Control and Polyhedral Approaches to PageRank Optimization." IEEE Transactions on Automatic Control 58, no. 1 (January 2013): 134–48. http://dx.doi.org/10.1109/tac.2012.2226103.

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Obikhod, Tetiana. "FORMATION OF MODERN MATHEMATICAL APPROACH TO SOLVING PROBLEMS OF PHYSICS." Physical and Mathematical Education 33, no. 1 (April 2, 2022): 26–29. http://dx.doi.org/10.31110/2413-1571-2022-033-1-004.

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Formulation of the problem. Precision studies of the Higgs boson, supersymmetric particles, the magnetic moment of the muon, electric dipole moment of the electron, flavor anomalies demonstrate the deviation beyond Standard Model. They are connected with a new understanding of quantum field theory through the unification of gravity with particle physics in the framework of string theory - the powerful instrument, which has changed the theory picture. The article is devoted to the study of new physics through these two components. First, we considered particle physics in terms of the latest experimental data and then moved on to the mathematical apparatus of string theory. Materials and methods. The N = 2 Yang-Mills theory is the heterotic string analog determined in ten-dimensional space: four usual space-time coordinates and six extra dimensions, known as Calabi-Yau manifold in weighted projective space. We studied the Calabi-Yau manifold in terms of both differential forms and reflexive polyhedrа to extract the elementary particle information. For further work with Calabi-Yau manifolds, differential forms for calculation of cohomology groups and reflexive polyhedrа for calculation of Hodge numbers were used. We used two definitions of general properties of toric varieties: hypersurfaces in terms of differential forms and projective space in terms of reflexive polyhedral. Then we investigated lattice polyhedra ∆ which gives rise to families of Calabi-Yau hypersurfaces in weighted projective space, P∆. Such polyhedra admit a combinatorial characterization and are called reflexive polyhedra. Results. The comparison of two approaches to the description of Calabi-Yau manifold as a complex manifold and as weighted projective space led us to the conclusion about the equivalence of these two treatments in the context of calculation of the Euler characteristic. As Euler’s characteristic for elementary particle physics is the number of generations of quarks and leptons, the selection of Calabi-Yau manifolds with appropriate topological properties is one of the urgent problems of modern physics. It is necessary to stress that the important result of our paper is the coincidence of the value of the Euler characteristic, found in terms of Dolbeault cohomology and terms of reflexive polyhedral. The obtained information about topological invariants is necessary for predicting the number of generations in particle physics. Conclusions. Although a unified theory of all interactions has not yet been found, however, certain aspects related to the interpretation of the unified theory of all interactions in terms of modern mathematics give their significant results. Therefore, the use and development of the apparatus of algebraic geometry for finding topological invariants that have the value of observables in physics is an urgent task.

Colombi, Marco, Renata Mansini, and Martin Savelsbergh. "The generalized independent set problem: Polyhedral analysis and solution approaches." European Journal of Operational Research 260, no. 1 (July 2017): 41–55. http://dx.doi.org/10.1016/j.ejor.2016.11.050.

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Carter, Paul. "Polyhedral: Recycling Boundary Ecologies." International Review of Information Ethics 11 (October 1, 2009): 45–51. http://dx.doi.org/10.29173/irie185.

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Foregrounding the extent to which 'place' remains resistant to the politics and poetics of 'network culture', this essay approaches place as a boundary ecology rather than as an instance of cultural invariance. It calls on readers to think about attempts to actively recycle cultural 'debris' or 'waste' through an ethics of passage instead of the kind of instrumentalist statics that prevents the development of an ontology of mobility. Contending that such a capacity to inhabit passage is compromised by the eschatological language used to communicate the implications of environmental disaster, as well as by languages of consultation that (conceptually) empty place of any creative power to incubate alternatives – events, modes of relation –, the essay stresses the mythopoetic techniques that produce places as knots or nodal points within a network of passage. The designer's task is to create the hinge mechanisms that render such boundary ecologies inhabitable imaginatively, and by materialising the nexus between creativity and change to alter our position vis-a-vis our ethical responsibilities as citizens of a shared biosphere.

Mousavi, Seyedahmad, та Jinglai Shen. "Solution uniqueness of convex piecewise affine functions based optimization with applications to constrained ℓ1 minimization". ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 56. http://dx.doi.org/10.1051/cocv/2018061.

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In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained ℓ1 recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of ℓ1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained ℓ1-minimization problems.

Schreiber, Thomas, Guido Brunnett, and Frank lsselhard. "Two approaches for polyhedral reconstruction of 3D objects of arbitrary genus." International Journal of Vehicle Design 21, no. 2/3 (1999): 292. http://dx.doi.org/10.1504/ijvd.1999.005581.

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Brimkov, Valentin E., and Reneta P. Barneva. "Graph-theoretic and polyhedral combinatorics issues and approaches in imaging sciences." Discrete Applied Mathematics 216 (January 2017): 321–22. http://dx.doi.org/10.1016/j.dam.2016.11.001.

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Zheng, Fei, Yu-Yong Jiao, Xi Zhang, Jia-He Lv, and Fei Tan. "Improved contact approaches for irregular polygonal or polyhedral blocks and their applications." IOP Conference Series: Earth and Environmental Science 861, no. 3 (October 1, 2021): 032033. http://dx.doi.org/10.1088/1755-1315/861/3/032033.

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Pringuey, Thibault, and R. Stewart Cant. "High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method." Communications in Computational Physics 12, no. 1 (July 2012): 1–41. http://dx.doi.org/10.4208/cicp.260511.050811a.

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AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

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Дисертації з теми "Polyhedral approaches":

Vandenbussche, Dieter. "Polyhedral approaches to solving nonconvex quadratic programs." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/23385.

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Miller, Andrew J. "Polyhedral approaches to capacitated lot-sizing problems." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24284.

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Pereira, Vargas Liguori Pedro. "Polyhedral approaches for some network design problems." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED074.

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Cette thèse étudie les aspects polyhédraux de certains problèmes de conception de réseau, en se concentrant principalement sur les aspects liés à la connectivité dessous-structures nécessaires pour créer des applications réseau fiables. Le cœur de nombreuses applications différentes de conception de réseau réside dans le fait qu’il est nécessaire de fournir un sous-réseau connexe (pouvant être compris comme un ensemble de sommets ou d’arêtes induisant un sous-graphe connecté) pouvant présenter d’autres propriétés souhaitables, comme atteindre un certain niveau de capacité de survie ou de robustesse, des contraintes de capacité ou d’autres types de contraintes budgétaires, en fonction du contexte. La plupart des études menées et des algorithmes développés tentent de tirer parti de ces aspects particuliers qui différencient une application de l’autre, sans se préoccuper des aspects qui réunissent ces questions. Par conséquent, ce travail tente de développer une approche unifiée capable d’explorer les aspects les plus pertinents des problèmes de conception de réseau, en espérant que cela conduirait à une compréhension réfléchie de problèmes plus spécifiques, en apportant une contribution précieuse à la recherche
This theses study the polyhedral aspects of some network design problems, focusing most on the aspects related to connectivity of the substructures necessary to build reliable network applications. At theheart of many different network design applications lies the fact that one must provide a connected subnetwork (which can be viewed as a collection of vertices or edges inducing a connected subgraph) exhibiting other desirable properties, like achieving some level of survivability or robustness, capacity constraints,or other types of budgetary constraints, depending on the context.A majority of the studies conductedand of the algorithms developed tryto take advantage of those particular aspects that differentiate one application from another, and not much attention has been given to the aspectsthat bring together these questions. Most of the studies conducted and the algorithms developed try to take advantage of those particular aspects that differentiate one application from another, and not much attention has been given to the aspects that bring together these questions. Hence, this work tries to develop an unified approach capable of exploring the most pertinent aspects of network design problems hoping that this can lead to thoughtful insights to more specific problems, being a valuable contribution to the research community and it

Waterer, Hamish. "Polyhedral approaches to scheduling shutdowns in production planning." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/23362.

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Zhang, Minjiao. "Polyhedral Approaches to Dynamic Decision Making under Uncertainty." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1373925091.

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Heilporn, Géraldine. "Network pricing problems : complexity, polyhedral study and solution approaches." Thèse, Universite Libre de Bruxelles, 2008. http://hdl.handle.net/1866/6451.

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Mesyagutov, Marat. "Exact Approaches for Higher-Dimensional Orthogonal Packing and Related Problems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-137905.

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NP-hard problems of higher-dimensional orthogonal packing are considered. We look closer at their logical structure and show that they can be decomposed into problems of a smaller dimension with a special contiguous structure. This decomposition influences the modeling of the packing process, which results in three new solution approaches. Keeping this decomposition in mind, we model the smaller-dimensional problems in a single position-indexed formulation with non-overlapping inequalities serving as binding constraints. Thus, we come up with a new integer linear programming model, which we subject to polyhedral analysis. Furthermore, we establish general non-overlapping and density inequalities and prove under appropriate assumptions their facet-defining property for the convex hull of the integer solutions. Based on the proposed model and the strong inequalities, we develop a new branch-and-cut algorithm. Being a relaxation of the higher-dimensional problem, each of the smaller-dimensional problems is also relevant for different areas, e.g. for scheduling. To tackle any of these smaller-dimensional problems, we use a Gilmore-Gomory model, which is a Dantzig-Wolfe decomposition of the position-indexed formulation. In order to obtain a contiguous structure for the optimal solution, its basis matrix must have a consecutive 1's property. For construction of such matrices, we develop new branch-and-price algorithms which are distinguished by various strategies for the enumeration of partial solutions. We also prove some characteristics of partial solutions, which tighten the slave problem of column generation. For a nonlinear modeling of the higher-dimensional packing problems, we investigate state-of-the-art constraint programming approaches, modify them, and propose new dichotomy and intersection branching strategies. To tighten the constraint propagation, we introduce new pruning rules. For that, we apply 1D relaxation with intervals and forbidden pairs, an advanced bar relaxation, 2D slice relaxation, and 1D slice-bar relaxation with forbidden pairs. The new rules are based on the relaxation by the smaller-dimensional problems which, in turn, are replaced by a linear programming relaxation of the Gilmore-Gomory model. We conclude with a discussion of implementation issues and numerical studies of all proposed approaches
Es werden NP-schwere höherdimensionale orthogonale Packungsprobleme betrachtet. Wir untersuchen ihre logische Struktur genauer und zeigen, dass sie sich in Probleme kleinerer Dimension mit einer speziellen Nachbarschaftsstruktur zerlegen lassen. Dies beeinflusst die Modellierung des Packungsprozesses, die ihreseits zu drei neuen Lösungsansätzen führt. Unter Beachtung dieser Zerlegung modellieren wir die Probleme kleinerer Dimension in einer einzigen positionsindizierten Formulierung mit Nichtüberlappungsungleichungen, die als Bindungsbedingungen dienen. Damit entwickeln wir ein neues Modell der ganzzahligen linearen Optimierung und unterziehen dies einer Polyederanalyse. Weiterhin geben wir allgemeine Nichtüberlappungs- und Dichtheitsungleichungen an und beweisen unter geeigneten Annahmen ihre facettendefinierende Eigenschaft für die konvexe Hülle der ganzzahligen Lösungen. Basierend auf dem vorgeschlagenen Modell und den starken Ungleichungen entwickeln wir einen neuen Branch-and-Cut-Algorithmus. Jedes Problem kleinerer Dimension ist eine Relaxation des höherdimensionalen Problems. Darüber hinaus besitzt es Anwendungen in verschiedenen Bereichen, wie zum Beispiel im Scheduling. Für die Behandlung der Probleme kleinerer Dimension setzen wir das Gilmore-Gomory-Modell ein, das eine Dantzig-Wolfe-Dekomposition der positionsindizierten Formulierung ist. Um eine Nachbarschaftsstruktur zu erhalten, muss die Basismatrix der optimalen Lösung die consecutive-1’s-Eigenschaft erfüllen. Für die Konstruktion solcher Matrizen entwickeln wir neue Branch-and-Price-Algorithmen, die sich durch Strategien zur Enumeration von partiellen Lösungen unterscheiden. Wir beweisen auch einige Charakteristiken von partiellen Lösungen, die das Hilfsproblem der Spaltengenerierung verschärfen. Für die nichtlineare Modellierung der höherdimensionalen Packungsprobleme untersuchen wir moderne Ansätze des Constraint Programming, modifizieren diese und schlagen neue Dichotomie- und Überschneidungsstrategien für die Verzweigung vor. Für die Verstärkung der Constraint Propagation stellen wir neue Ablehnungskriterien vor. Wir nutzen dabei 1D Relaxationen mit Intervallen und verbotenen Paaren, erweiterte Streifen-Relaxation, 2D Scheiben-Relaxation und 1D Scheiben-Streifen-Relaxation mit verbotenen Paaren. Alle vorgestellten Kriterien basieren auf Relaxationen durch Probleme kleinerer Dimension, die wir weiter durch die LP-Relaxation des Gilmore-Gomory-Modells abschwächen. Wir schließen mit Umsetzungsfragen und numerischen Experimenten aller vorgeschlagenen Ansätze

Oosten, Maarten. "A polyhedral approach to grouping problems." [Maastricht : Maastricht : Universiteit Maastricht] ; University Library, Maastricht University [Host], 1996. http://arno.unimaas.nl/show.cgi?fid=6706.

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Arambula, Mercado Ivette. "A new polyhedral approach to combinatorial designs." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/358.

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We consider combinatorial t-design problems as discrete optimization problems. Our motivation is that only a few studies have been done on the use of exact optimization techniques in designs, and that classical methods in design theory have still left many open existence questions. Roughly defined, t-designs are pairs of discrete sets that are related following some strict properties of size, balance, and replication. These highly structured relationships provide optimal solutions to a variety of problems in computer science like error-correcting codes, secure communications, network interconnection, design of hardware; and are applicable to other areas like statistics, scheduling, games, among others. We give a new approach to combinatorial t-designs that is useful in constructing t-designs by polyhedral methods. The first contribution of our work is a new result of equivalence of t-design problems with a graph theory problem. This equivalence leads to a novel integer programming formulation for t-designs, which we call GDP. We analyze the polyhedral properties of GDP and conclude, among other results, the associated polyhedron dimension. We generate new classes of valid inequalities to aim at approximating this integer program by a linear program that has the same optimal solution. Some new classes of valid inequalities are generated as Chv´atal-Gomory cuts, other classes are generated by graph complements and combinatorial arguments, and others are generated by the use of incidence substructures in a t-design. In particular, we found a class of valid inequalities that we call stable-set class that represents an alternative graph equivalence for the problem of finding a t-design. We analyze and give results on the strength of these new classes of valid inequalities. We propose a separation problem and give its integer programming formulation as a maximum (or minimum) edge-weight biclique subgraph problem. We implement a pure cutting-plane algorithm using one of the stronger classes of valid inequalities derived. Several instances of t-designs were solved efficiently by this algorithm at the root node of the search tree. Also, we implement a branch-and-cut algorithm and solve several instances of 2-designs trying different base formulations. Computational results are included.

Wu, Xiaolin. "A polyhedral approach to designing communication networks." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/9917.

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Polytopes $Q\sbsp{2E}{n}$ and $Q\sbsp{2N}{n}$, which are associated with the minimum cost 2-edge-connected subgraph problem and the minimum cost 2-node-connected subgraph problem, respectively, are studied in this thesis, and some new classes of facet-inducing inequalities are introduced for these polytopes. These classes of inequalities are related to the so-called clique tree inequalities for the travelling salesman polytope ($Q\sbsp{T}{n}$), and the relationships between $Q\sbsp{T}{n}$ and $Q\sbsp{2E}{n}, Q\sbsp{2N}{n}$ are exploited in obtaining these new classes of facets. Due to the use of problem specific facet-inducing inequalities instead of dominant cutting-planes, the linear programming cutting-plane method has proven to be quite successful for solving some NP-hard combinatorial optimization problems. We believe that our new classes of facet-inducing inequalities can be used to further improve the cutting-plane procedure for designing minimum cost survivable communication networks.

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Книги з теми "Polyhedral approaches":

Pugh, Anthony. Polyhedra: A visual approach. Palo Alto, CA: Dale Seymour Publications, 1990.

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M, Milanese, ed. Bounding approaches to system identification. New York: Plenum Press, 1996.

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Milanese, M. Bounding Approaches to System Identification. Springer, 2013.

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Marjorie, Senechal, Fleck George M, and Shaping Space Conference (1984 : Smith College), eds. Shaping space: A polyhedral approach. Boston: Birkhäuser, 1988.

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Senechal, Marjorie. Shaping Space: A Polyhedral Approach (Design Science Collection). Birkhauser, 1988.

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Частини книг з теми "Polyhedral approaches":

Mahjoub, Ali Ridha. "Polyhedral Approaches." In Concepts of Combinatorial Optimization, 261–324. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118600245.ch10.

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Mahjoub, Ali Ridha. "Polyhedral Approaches." In Concepts of Combinatorial Optimization, 261–324. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781119005216.ch10.

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King, R. B. "Polyhedral Dynamics." In Graph Theoretical Approaches to Chemical Reactivity, 109–35. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1202-4_4.

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Grötschel, M., C. Monma, and M. Stoer. "Polyhedral approaches to network survivability." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 121–42. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/005/08.

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Conforti, Michele, Gérard Cornuéjols, and Giacomo Zambelli. "Polyhedral Approaches to Mixed Integer Linear Programming." In 50 Years of Integer Programming 1958-2008, 343–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-68279-0_11.

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Kammer, Frank, Maarten Löffler, Paul Mutser, and Frank Staals. "Practical Approaches to Partially Guarding a Polyhedral Terrain." In Geographic Information Science, 318–32. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11593-1_21.

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Chopra, Sunil, and Chih-Yang Tsai. "Polyhedral Approaches for the Steiner Tree Problem on Graphs." In Combinatorial Optimization, 175–201. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0255-1_5.

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Piet-Lahanier, H., and É. Walter. "Limited-Complexity Polyhedric Tracking." In Bounding Approaches to System Identification, 261–73. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-9545-5_16.

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Bobenko, Alexander I., Christian Mercat, and Markus Schmies. "Period Matrices of Polyhedral Surfaces." In Computational Approach to Riemann Surfaces, 213–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-17413-1_7.

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Martin, Richard Kipp. "Interior Point Algorithms: Polyhedral Transformations." In Large Scale Linear and Integer Optimization: A Unified Approach, 219–60. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-4975-8_7.

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Тези доповідей конференцій з теми "Polyhedral approaches":

Agarwal, Y. K. "Survivable network design using polyhedral approaches." In 2011 Third International Conference on Communication Systems and Networks (COMSNETS 2011). IEEE, 2011. http://dx.doi.org/10.1109/comsnets.2011.5716411.

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Maza, Stéphane, Jean-Claude Léon, and Frédéric Noël. "Mesh Construction Dedicated to a Multi-Representation for Structure Analysis Based on an Initial Polyhedral Geometry." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/cie-4446.

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Abstract The aim of this paper is to present the first part of a new approach devoted to the generation of a data structure and operators for the hierarchical representation of 3D polyhedra. Here are described the treatments which allow to create some of the elements of this hierarchical model. At first, partitions of the initial polyhedron are mapped into planar connex hulls. Then, these domains are used like a piecewise parametric 2D space for subsequent polyhedra generations. In order to create such a mapping, the initial 3D polyhedron is partitioned to produce simply convex subsets which can be submitted to the parametrization process. The next step consists in the generation of a minimum representation of the initial 3D polyhedron. This representation forms the root of the hierarchical data structure. Then, the mapping obtained allows the construction of various polyhedral representations of the initial geometry. Criteria related to 3D parameters are used to generate the range of polyhedra. The reverse mapping (from 2D to 3D) helps reduce the computing cost required to generate 3D polyhedra. Each 3D polyhedron generation is carried out under 3D geometric criteria depending on the context. i.e.: structural analysis, levels of details of a geometric model, ... Among the goals of the hierarchical data structure, the unification and the inter dependency of the meshes required to carry out the structural analysis of a part occupies a central position.

Delos, Vincent, Santiago Arroyave-Tobón, and Denis Teissandier. "Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85366.

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In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

Zhang, Ying, Hai-Jun Su, Qizheng Liao, Shimin Wei, and Weiqing Li. "New Synthesis Approach for Expandable Polyhedral Linkages." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35114.

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This paper presents a new synthesis approach for expandable polyhedral linkages, which are synthesized by inserting appropriate link groups into the faces of polyhedron and interconnecting them by a special composite hinges (called gusset by K. Wohlhart). The overconstrained expandable polyhedral linkages are movable with one degree of freedom (DOF).The link groups are single DOF scaling planar linkages. The gussets are multiple rotary joints whose axes converge at the corresponding vertices of the polyhedron and the number of the rotary joints equals the one of the faces which meet at the vertices. This new approach is suitable for any polyhedron whatever is regular or irregular polyhedron. To verify this new approach, the expandable regular hexahedral linkage is modeled in the SolidWorks and its mobility are studied based on screw theory and topology graph.

Heal, Maher Hashem. "Simple Proofs of the Strong Perfect Graph Theorem Using Polyhedral Approaches and Proving P=NP as a Conclusion." In 2020 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2020. http://dx.doi.org/10.1109/csci51800.2020.00274.

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Liu, C. Y., and R. W. Mayne. "Distance Calculations in Motion Planning Problems With Interference Situations." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0018.

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Abstract This paper discusses distance calculations for three dimensional polyhedra with the assumption of convex bodies. An n-surface convex polyhedron is viewed as the intersection of n half-spaces and is represented by n linear inequality equations while the square of the distance between two points is of a quadratic form in terms of two sets of x-y-z coordinates. The static distance-to-contact between two non-interfering convex polyhedral shapes is then directly solvable by quadratic programming. Based on the concept of distance-past-contact, distance calculations for situations with interference are presented and tested in optimization based robot path planning examples. The distance evaluation is further investigated for the dynamic situations by a swept volume computation strategy. The approach is illustrated in examples with a moving robot link and a fixed obstacle.

Honarpardaz, Mohammadali, Mehdi Tarkian, Xiaolong Feng, Daniel Sirkett, and Johan Ölvander. "Generic Automated Finger Design." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60514.

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Finger design automation for grippers is one of the areas of highest interest for robot industries. The few studies that have been carried out in the finger design automation research area are limited to objects with specific geometrical properties (e.g. polyhedral). This paper introduces the Generic Automated Finger Design (GAFD) method that contains the essential key processes for automatic design of reliable fingers. The proposed method is implemented on two geometrically complex workpieces and appropriate fingers are designed. The results are discussed in detail and benchmarked against existing approaches.

Morrison, James R., and P. R. Kumar. "Linear Programming Performance Bounds for Markov Chains With Polyhedrally Translation Invariant Probabilities and Applications to Unreliable Manufacturing Systems and Enhanced Wafer Fab Models." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39274.

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Our focus is on a class of Markov chains which have a polyhedral translation invariance property for the transition probabilities. This class can be used to model several applications of interest which feature complexities not found in usual models of queueing networks, for example failure prone manufacturing systems which are operating under hedging point policies, or enhanced wafer fab models featuring batch tools and setups or affine index policies. We present a new family of performance bounds which is more powerful both in expressive capability as well as the quality of the bounds than some earlier approaches.

Mishra, Amitesh, and Anupam Saxena. "On Preliminaries of 3D Solid Reconstruction Using Auxiliary Views." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84230.

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In this paper is proposed a method to reconstruct a solid from given two or three orthographic views along with any number of primary auxiliary views based on the combination of wireframe and volumetric approaches. None of the existing works in automatic reconstruction of solids from two dimensional orthographic views have addressed auxiliary views in detail. Polyhedral approximation of cylindrical, conical, toroidal and spherical surfaces is considered. The algorithm presented, entails the construction of the basic wire-frame from given standard views using the wire-frame approach. The projections in the auxiliary views on the basic orthographic views are swept along the projection lines to form the primitives. These primitives are glued to the basic wire-frame to construct the final solid. Numerous examples are presented in this paper to demonstrate the versatility of the proposed method which can handle partial standard and auxiliary views as well.

Verma, Ishan, Laith Zori, Jaydeep Basani, and Samir Rida. "Modeling of Combustor and Turbine Vane Interaction." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90325.

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Abstract Modern aero-engines are characterized by compact components (fan, compressor, combustor, and turbine). Such proximity creates a complex interaction between the components and poses a modeling challenge due to the difficulties in identifying a clear interface between components since they are usually modeled separately. From a numerical point of view, the simulation of a complex compact aero-engine system requires interaction between these individual components, especially the combustor-turbine interaction. The combustor is characterized by a subsonic chemically reacting and swirling flow while the high-pressure turbine (HPT) stage has flow which is transonic. Furthermore, the simulation of combustor-turbine interactions is more challenging due to aggressive flow conditions such as non-uniform temperature, non-uniform total-pressure, strong swirl, and high turbulence intensity. The simulation of aero-engines, where combustor-turbine interactions are important, requires a methodology that can be used in a real engine framework while ensuring numerical requirements of accuracy and stability. Conventionally, such a simulation is carried out using one of the two approaches: a combined simulation (or joint-simulation) of the combustor and the HPT geometries, or a co-simulation between the combustor and the turbine with the exchange of boundary conditions between these two separate domains. The primary objective of this paper is to assess the effectiveness of the joint simulation versus the co-simulation and propose a more practical approach for modeling combustor and turbine interactions. First, a detailed grid independence study with hexahedral and polyhedral meshes is performed to select the required polyhedral mesh. Then, an optimal location of the interface between the combustor and the nozzle guide vane (NGV) is identified. Co-simulations are then performed by exchanging information between the combustor and the NGV at the interface, wherein the combustor is solved using LES while the NGV is solved using RANS. The joint combustor-NGV simulations are solved using LES. The effect of the combustor-NGV interaction on the flow field and hot streak migration is analyzed. The results suggest that the joint simulation is computationally efficient and more accurate since both components are modelled together.