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Rozprawy doktorskie na temat „Semidefinite programming”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Zhu, Yuntao. "Semidefinite programming under uncertainty." Online access for everyone, 2006. http://www.dissertations.wsu.edu/Dissertations/summer2006/y%5Fzhu%5F073106.pdf.

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2

Jibrin, Shafiu. "Redundancy in semidefinite programming." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0010/NQ32337.pdf.

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3

Jibrin, Shafiu Carleton University Dissertation Mathematics and Statistics. "Redundancy in semidefinite programming." Ottawa, 1997.

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4

Wei, Hua. "Numerical Stability in Linear Programming and Semidefinite Programming." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2922.

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We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms. <br /><br /> We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10<sup>-8</sup> when the

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5

Zanjácomo, Paulo Régis. "On weighted paths for nonlinear semidefinite complementarity problems and newton methods for semidefinite programming." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/21680.

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6

Ye, Kai. "Applications of semidefinite programming in finance." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.508489.

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7

Keuchel, Jens. "Image partitioning based on semidefinite programming." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11513861.

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8

Qian, Xun. "Continuous methods for convex programming and convex semidefinite programming." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/422.

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In this thesis, we study several interior point continuous trajectories for linearly constrained convex programming (CP) and convex semidefinite programming (SDP). The continuous trajectories are characterized as the solution trajectories of corresponding ordinary differential equation (ODE) systems. All our ODE systems are closely related to interior point methods.. First, we propose and analyze three continuous trajectories, which are the solutions of three ODE systems for linearly constrained convex programming. The three ODE systems are formulated based on an variant of the affine scaling

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9

Shen, Yijiang. "Binary image restoration by positive semidefinite programming and signomial programming." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39557431.

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10

沈逸江 and Yijiang Shen. "Binary image restoration by positive semidefinite programming and signomial programming." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39557431.

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11

Zhao, Qing. "Semidefinite programming for assignment and partitioning problems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21405.pdf.

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12

Stovall, Kazumi Niki. "Semidefinite Programming and Stability of Dynamical System." Digital Archive @ GSU, 2006. http://digitalarchive.gsu.edu/math_theses/4.

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In the first part of the thesis we present several interior point algorithms for solving certain positive definite programming problems. One of the algorithms is adapted for finding out whether there exists or not a positive definite matrix which is a real linear combination of some given symmetric matrices A1,A2, . . . ,Am. In the second part of the thesis we discuss stability of nonlinear dynamical systems. We search using algorithms described in the first part, for Lyapunov functions of a few forms. A suitable Lyapunov function implies the existence of a hyperellipsoidal attraction region f

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13

Biswas, Pratik. "Semidefinite programming approaches to distance geometry problems /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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14

Lopez, Rafaël. "Stochastic quadratic knapsack problems and semidefinite programming." Paris 11, 2009. http://www.theses.fr/2009PA112283.

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Dans cette thèse, nous présentons une étude détaillée de problèmes de sac-à-dos stochastiques quadratiques, ainsi que des applications de la Programmation Semidéfinie (SDP) pour un problème de télécommunications et pour une étude expérimentale pour des problèmes de Coupe Max et de CDMA. La première partie de cette thèse consiste en un rappel des notions et résultats utilisés par la suite. La seconde partie est consacrée à l’étude du problème du sac- à- dos stochastique, dont nous développons un nouveau modèle, à deux phases (recours) et à contraintes probabilistes. Nous en proposons plusieurs

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15

Fantuzzi, Giovanni. "Construction of optimal background fields using semidefinite programming." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/60642.

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Quantitative analysis of systems exhibiting turbulence is challenging due to the lack of exact solutions and the cost of accurate simulations, but asymptotic or time-averaged properties can often be bounded rigorously using the background method. This rests on the construction of a background field for the system subject to a spectral constraint, which requires that a background-field-dependent linear operator has non-negative eigenvalues. This thesis develops techniques for the numerical optimisation of background fields and their corresponding bounds. First, bounds on the asymptotic energy o

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16

Yan, Zhifei. "Semidefinite Programming Approaches to Network Clustering and Smoothing." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503180139155502.

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17

Naldi, Simone. "Exact algorithms for determinantal varieties and semidefinite programming." Thesis, Toulouse, INSA, 2015. http://www.theses.fr/2015ISAT0021/document.

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Dans cette thèse, nous nous intéressons à l'étude des structures déterminantielles apparaissent dans l'optimisation semi-définie (SDP), le prolongement naturel de la programmation linéaire au cône des matrices symétrique semi-définie positives. Si l'approximation d'une solution d'un programme semi-défini peut être calculé efficacement à l'aide des algorithmes de points intérieurs, ni des algorithmes exacts efficaces pour la SDP sont disponibles, ni une compréhension complète de sa complexité théorique a été atteinte. Afin de contribuer à cette question centrale en optimisation convexe, nous co

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18

Han, Weiqiao. "Semidefinite programming approaches to multi-contact feedback control." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122698.

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This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 71-77).<br>We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We examine

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19

Lu, Zhaosong. "Algorithm Design and Analysis for Large-Scale Semidefinite Programming and Nonlinear Programming." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7151.

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The limiting behavior of weighted paths associated with the semidefinite program (SDP) map $X^{1/2}SX^{1/2}$ was studied and some applications to error bound analysis and superlinear convergence of a class of primal-dual interior-point methods were provided. A new approach for solving large-scale well-structured sparse SDPs via a saddle point mirror-prox algorithm with ${cal O}(epsilon^{-1})$ efficiency was developed based on exploiting sparsity structure and reformulating SDPs into smooth convex-concave saddle point problems. An iterative solver-based long-step primal-dual infeasible path-fo

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20

Macedo, Eloísa Catarina Monteiro de Figueiredo Amaral e. "Numerical study of regularity in semidefinite programming and applications." Doctoral thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/16278.

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Doutoramento em Matemática<br>This thesis is devoted to the study of regularity in semidefinite programming (SDP), an important area of convex optimization with a wide range of applications. The duality theory, optimality conditions and methods for SDP rely on certain assumptions of regularity that are not always satisfied. Absence of regularity, i.e., nonregularity, may affect the characterization of optimality of solutions and SDP solvers may run into numerical difficulties, leading to unreliable results. There exist different notions associated to regularity. In this thesis, we stud

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21

Yamakawa, Yuya. "Studies on Optimization Methods for Nonlinear Semidefinite Programming Problems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199446.

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22

Li, Chao. "Semidefinite programming, binary codes and a graph coloring problem." Digital WPI, 2015. https://digitalcommons.wpi.edu/etd-theses/863.

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"Experts in information theory have long been interested in the maximal size, A(n, d), of a binary error-correcting code of length n and minimum distance d, The problem of determining A(n, d) involves both the construction of good codes and the search for good upper bounds. For quite some time now, Delsarte's linear programming approach has been the dominant approach to obtaining the strongest general purpose upper bounds on the efficiency of error-correcting codes. From 1973 forward, the linear programming bound found many applications, but there were few significant theoretical advances unti

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23

Monir, Vaghefi Sayed Reza. "Cooperative Positioning in Wireless Sensor Networks Using Semidefinite Programming." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/71884.

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With the rapid development of wireless technologies, the demand for positioning services has grown dramatically over the past three decades. The Global Positioning System (GPS) is widely used in wireless devices for positioning purposes. However, in addition to having bulky and expensive equipment, GPS receivers do not operate properly in dense and indoor environments. Difficulties in using GPS lead us to use sensor localization in which the position information is obtained from the measurements collected within the network without the aid of external resources. Sensor localization has been a

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24

Mefo, Kue Floriane. "Mixed integer bilevel programming problems." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2017. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-230335.

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This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. Afte

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25

Salinas, Varela Adrián Alberto. "Semidefinite programming-based analysis of continuous-time piecewise affine systems." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608522.

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26

Dowdy, Garrett Ryan. "Using semidefinite programming to bound distributions in chemical engineering systems." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/121820.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 329-334).<br>Distributions appear in many forms in models of chemical engineering systems. Such distributions account for microscopic variability in the system while simultaneously explaining its macroscopic properties. These macroscopic properties are often of practical engineering interest. Thus, it is valuable to be able to characterize the underlying distributions that affect them. Recently, in the mathematica

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27

Skomra, Mateusz. "Tropical spectrahedra : Application to semidefinite programming and mean payoff games." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX058/document.

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La programmation semi-définie est un outil fondamental d'optimisation convexe et polynomiale. Elle revient à optimiser une fonction linéaire sur un spectraèdre (un ensemble défini par des inégalités matricielles linéaires). En particulier, la programmation semi-définie est une généralisation de la programmation linéaire.Nous étudions l'analogue non-archimédien de la programmation semi-définie, en remplaçant le corps des nombres réels par le corps des séries de Puiseux. Notre approche est fondée sur des méthodes issues de la géométrie tropicale et, en particulier, sur l'étude de la tropicalisat

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28

Oskoorouchi, Mohammad R. "The analytic center cutting plane method with semidefinite cuts /." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=38507.

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We propose an analytic center cutting plane algorithm for semidefinite programming (SDP). Reformulation of the dual problem of SDP into an eigenvalue optimization, when the trace of any feasible primal matrix is a positive constant, is well known. We transform the eigenvalue optimization problem into a convex feasibility problem. The problem of interest seeks a feasible point in a bounded convex set, which contains a full dimensional ball with &egr;(<1) radius and is contained in a compact convex set described by matrix inequalities, known as the set of localization. At each iteration, an appr

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29

Jiao, Chunxi. "Semidefinite relaxations for a linear programming approach to exit-time stochastic control." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/24569.

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In this thesis, we investigate the linear programming framework for exit-time stochastic control problems and apply the moment-sum-of-squares (moment-SOS) hierarchy to obtain convergent pointwise bounds and global bounding functions for the value functions. The primal linear program over suitable measures and the dual linear program over continuous test functions are implemented numerically by semidefinite programs which target moments and SOS polynomial representations respectively. Numerically optimised bounds converge to the value function from below as polynomial degree increases under sui

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30

Burer, Samuel A. "New algorithmic approaches for semidefinite programming with applications to combinatorial optimization." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/30268.

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31

Gong, Yun. "On semidefinite programming and vector quantization with application to image coding." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/14876.

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32

Kim, Chiheon. "Statistical limits of graphical channel models and a semidefinite programming approach." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120659.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 205-213).<br>Community recovery is a major challenge in data science and computer science. The goal in community recovery is to find the hidden clusters from given relational data, which is often represented as a labeled hyper graph where nodes correspond to items needing to be labeled and edges correspond to observed relations between the items. We investigate the problem of exact recovery in the class of statistical mod

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33

Hu, Sha S. M. Massachusetts Institute of Technology. "Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39217.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.<br>Includes bibliographical references (leaves 73-75).<br>In this thesis, we use a semidefinite relaxation based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to solve nonconvex Box constrained Quadratic Programming (BoxQP) problems and the comparison of the four methods. For some lower dimension

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34

Ha, Hoang Kha Electrical Engineering &amp Telecommunications Faculty of Engineering UNSW. "Linear phase filter bank design by convex programming." Publisher:University of New South Wales. Electrical Engineering & Telecommunications, 2008. http://handle.unsw.edu.au/1959.4/43268.

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Digital filter banks have found in a wide variety of applications in data compression, digital communications, and adaptive signal processing. The common objectives of the filter bank design consist of frequency selectivity of the individual filters and perfect reconstruction of the filter banks. The design problems of filter banks are intrinsically challenging because their natural formulations are nonconvex constrained optimization problems. Therefore, there is a strong motivation to cast the design problems into convex optimization problems whose globally optimal solutions can be efficientl

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35

Habermehl, Kai [Verfasser]. "Robust optimization of active trusses via mixed-integer semidefinite programming / Kai Habermehl." München : Verlag Dr. Hut, 2014. http://d-nb.info/1058285092/34.

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36

Passuello, Alberto. "Semidefinite programming in combinatorial optimization with applications to coding theory and geometry." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00948055.

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We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence

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Yeung, Sai Hei. "Analysis of the Projective Re-Normalization method on semidefinite programming feasibility problems." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43800.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008.<br>Includes bibliographical references (p. 75-76).<br>In this thesis, we study the Projective Re-Normalization method (PRM) for semidefinite programming feasibility problems. To compute a good normalizer for PRM, we propose and study the advantages and disadvantages of a Hit & Run random walk with Dikin ball dilation. We perform this procedure on an ill-conditioned two dimensional simplex to show the Dikin ball Hit & Run random walk mixes much faster than standard Hit & Run random walk.

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38

Fawzi, Hamza. "Power and limitations of convex formulations via linear and semidefinite programming lifts." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/107331.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 155-162).<br>Convex relaxation methods play an important role in mathematical optimization to tackle hard nonconvex problems, and have been applied successfully in many areas of science and engineering. At the heart of such methods lies the question of obtaining a tractable description of the convex hull of a set. In this thesis we focus on the question of finding tractable representations

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39

Mars, Sonja [Verfasser]. "Mixed-Integer Semidefinite Programming with an Application to Truss Topology Design / Sonja Mars." München : Verlag Dr. Hut, 2013. http://d-nb.info/1037286774/34.

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40

Kleniati, Polyxeni M. "Decomposition schemes for polynomial optimisation, semidefinite programming and applications to nonconvex portfolio decisions." Thesis, Imperial College London, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509792.

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Adasme, Soto Pablo Alberto. "Deterministic uncertain nonlinear formulations for wireless OFDMA networks with applications on semidefinite programming." Paris 11, 2010. http://www.theses.fr/2010PA112323.

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Dans cette thèse, on étudie l'utilisation de la programmation semi-définie (SDP), l'optimisation robuste, la programmation stochastique, les relaxations lagrangiennes et des approches polyédriques de traitement de l'incertitude pour résoudre le problème d'allocation de ressources dans les réseaux sans fil OFDMA. Le premier chapitre introduit ce problème d'allocation de ressources. Puis, on fournit dans le chapitre 2 un bref aperçu théorique des concepts et méthodes dont on aura besoin dans la suite de la thèse. Dans le chapitre 3, les principales formulations mathématiques de la littérature li

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42

So, Anthony Man-Cho. "A semidefinite programming approach to the graph realization problem : theory, applications and extensions /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Fortin, Charles. "A survey of the trust region subproblem within a semidefinite framework." Thesis, University of Waterloo, 2000. http://hdl.handle.net/10012/1038.

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Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of different methods developed to find an approximate solution to the subproblem. We study the well-known method of More and Sorensen and two recent methods for large sparse subproblems: the so-called Lanczos method of Gould et al. and the Rendland Wolkowicz algorithm. The common ground to explore these methods will be semidefinite programming. This approach has been used

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44

Yang, Shaoshi. "Detection for multiple-input multiple-output systems : probabilistic data association and semidefinite programming relaxation." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/360710/.

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As a highly effective physical-layer interference management technique, the joint detection of a vector of non-orthogonal information-bearing symbols simultaneously transmitted over multiple-input multiple-output (MIMO) channels is of fundamental importance for high throughput digital communications. This is because the generic mathematical model of MIMO detection underpins a wide range of relevant applications including (but not limited to) the equalization of dispersive band-limited channels imposing intersymbol interference (ISI), the multiuser detection (MUD) in code-division multiple-acce

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45

ONO, Takao, and Tomio HIRATA. "Approximation Algorithms for MAX SAT." Institute of Electronics, Information and Communication Engineers, 2000. http://hdl.handle.net/2237/15068.

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46

Fraticelli, Barbara M. P. "Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/27293.

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This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on a

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47

Yang, Boshi. "A conic optimization approach to variants of the trust region subproblem." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1938.

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The Trust Region Subproblem (TRS), which minimizes a nonconvex quadratic function over the unit ball, is an important subproblem in trust region methods for nonlinear optimization. Even though TRS is a nonconvex problem, it can be solved in polynomial time using, for example, a semidefinite programming (SDP) relaxation. Different variants of TRS have been considered from both theoretical and practical perspectives. In this thesis, we study three variants of TRS and their SDP/conic relaxations. We first study an extended trust region subproblem (eTRS) in which the trust region equals the inters

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48

ROJAS, JHONATAN EDWAR GARCIA. "NUMERICAL LIMIT ANALYSIS USING SEMIDEFINITE AND SECOND ORDER CONIC PROGRAMMING WITH APPLICATION IN STABILITY OF SHALLOW TUNNELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36904@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>Nesse trabalho é avaliada a solução numérica do colapso na frente de escavação em túneis rasos, através da teoria de análise limite numérico, usando o teorema do limite inferior, a partir da condição de equilíbrio para as condições plásticas, além de considerar o comportamento do material rígido perfeitamente plástico. O teorema de limite inferior implica em maximizar o fator multiplicador na carga atuante, por isso a análise limite se torna

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Evangelista, Tatiane da Silva. "Discriminação de estados quanticos via programação semidefinida." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306810.

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Orientadores: Carlile Campos Lavor, Wilson Ricardo Matos Rabelo<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-13T05:05:06Z (GMT). No. of bitstreams: 1 Evangelista_TatianedaSilva_D.pdf: 1204224 bytes, checksum: 78ba86ca8ac235e2775ed6a048ccf353 (MD5) Previous issue date: 2009<br>Resumo: Neste trabalho, apresentamos um novo algoritmo para realizar a discriminação ótima de N estados quânticos puros não-ortogonais, que fornece o melhor conjunto de medidas POVM para o problema, através d

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Machado, Fabrício Caluza. "Limitantes de programação semidefinida para o número de contato." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-17052017-225346/.

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O número de contato do Rn (em inglês, kissing number) é o maior número de esferas de raio unitário e interiores dois-a-dois disjuntos que podem tocar simultaneamente uma esfera de raio unitário central. Nesta dissertação estudamos métodos que limitam o tamanho de tais configurações através de técnicas de otimização, como dualidade e programação semidefinida. O principal resultado obtido foi o cálculo de melhores limitantes para o número de contato nas dimensões 9 a 23; o que foi possível graças à exploração de simetrias dos polinômios presentes no limitante proposto por Bachoc e Vallentin (200

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