دانلود کتاب خارجی - دانلود رایگان کتاب لاتین PDF علمی

تعداد نتایج: 338

2000
Language: de
OTHER:OCLC:1414986409

Convex Optimization & Euclidean Distance Geometry

$The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs has already proven invaluable in discerning biological molecular conformation.The emerging practice of localization in wireless sensor networks, the global positioning system (GPS), and distance-based pattern recognitionwill certainly simplify and benefit from this theory.We study the pervasive convex Euclidean bodies and their various representations.In particular, we make convex polyhedra, cones, and dual cones more visceral through illustration, andwe study the geometric relation of polyhedral cones to nonorthogonal bases biorthogonal expansion.We explain conversion between halfspace- and vertex-descriptions of convex cones,we provide formulae for determining dual cones,and we show how classic alternative systems of linear inequalities or linear matrix inequalities and optimality conditions can be explained by generalized inequalities in terms of convex cones and their duals.The conic analogue to linear independence, called conic independence, is introducedas a new tool in the study of classical cone theory; the logical next step in the progression:linear, affine, conic.Any convex optimization problem has geometric interpretation.This is a powerful attraction: the ability to visualize geometry of an optimization problem.We provide tools to make visualization easier.The concept of faces, extreme points, and extreme directions of convex Euclidean bodiesis explained here, crucial to understanding convex optimization.The convex cone of positive semidefinite matrices, in particular, is studied in depth.We mathematically interpret, for example,its inverse image under affine transformation, and we explainhow higher-rank subsets of its boundary united with its interior are convex.The Chapter on "Geometry of convex functions",observes analogies between convex sets and functions:The set of all vector-valued convex functions is a closed convex cone.Included among the examples in this chapter, we show how the real affinefunction relates to convex functions as the hyperplane relates to convex sets.Here, also, pertinent results formultidimensional convex functions are presented that are largely ignored in the literature;tricks and tips for determining their convexityand discerning their geometry, particularly with regard to matrix calculus which remains largely unsystematizedwhen compared with the traditional practice of ordinary calculus.Consequently, we collect some results of matrix differentiation in the appendices.The Euclidean distance matrix (EDM) is studied,its properties and relationship to both positive semidefinite and Gram matrices.We relate the EDM to the four classical axioms of the Euclidean metric;thereby, observing the existence of an infinity of axioms of the Euclidean metric beyondthe triangle inequality. We proceed byderiving the fifth Euclidean axiom and then explain why furthering this endeavoris inefficient because the ensuing criteria (while describing polyhedra)grow linearly in complexity and number.Some geometrical problems solvable via EDMs,EDM problems posed as convex optimization, and methods of solution arepresented;\eg, we generate a recognizable isotonic map of the United States usingonly comparative distance information (no distance information, only distance inequalities).We offer a new proof of the classic Schoenberg criterion, that determines whether a candidate matrix is an EDM. Our proofrelies on fundamental geometry; assuming, any EDM must correspond to a list of points contained in some polyhedron(possibly at its vertices) and vice versa.It is not widely known that the Schoenberg criterion implies nonnegativity of the EDM entries; proved here.We characterize the eigenvalues of an EDM matrix and then devisea polyhedral cone required for determining membership of a candidate matrix(in Cayley-Menger form) to the convex cone of Euclidean distance matrices (EDM cone); \ie,a candidate is an EDM if and only if its eigenspectrum belongs to a spectral cone for EDM^N.We will see spectral cones are not unique.In the chapter "EDM cone", we explain the geometric relationship betweenthe EDM cone, two positive semidefinite cones, and the elliptope.We illustrate geometric requirements, in particular, for projection of a candidate matrixon a positive semidefinite cone that establish its membership to the EDM cone. The faces of the EDM cone are described,but still open is the question whether all its faces are exposed as they are for the positive semidefinite cone.The classic Schoenberg criterion, relating EDM and positive semidefinite cones, isrevealed to be a discretized membership relation (a generalized inequality, a new Farkas''''''''-like lemma)between the EDM cone and its ordinary dual. A matrix criterion for membership to the dual EDM cone is derived thatis simpler than the Schoenberg criterion.We derive a new concise expression for the EDM cone and its dual involvingtwo subspaces and a positive semidefinite cone."Semidefinite programming" is reviewedwith particular attention to optimality conditionsof prototypical primal and dual conic programs,their interplay, and the perturbation method of rank reduction of optimal solutions(extant but not well-known).We show how to solve a ubiquitous platonic combinatorial optimization problem from linear algebra(the optimal Boolean solution x to Ax=b)via semidefinite program relaxation.A three-dimensional polyhedral analogue for the positive semidefinite cone of 3X3 symmetricmatrices is introduced; a tool for visualizing in 6 dimensions.In "EDM proximity"we explore methods of solution to a few fundamental and prevalentEuclidean distance matrix proximity problems; the problem of finding that Euclidean distance matrix closestto a given matrix in the Euclidean sense.We pay particular attention to the problem when compounded with rank minimization.We offer a new geometrical proof of a famous result discovered by Eckart \& Young in 1936 regarding Euclideanprojection of a point on a subset of the positive semidefinite cone comprising all positive semidefinite matriceshaving rank not exceeding a prescribed limit rho.We explain how this problem is transformed to a convex optimization for any rank rho.$

جزئیات و درخواست

By Jon Dattorro
Publisher: Meboo Publishing USA, 2005
Pages: 776
Language: en
ISBN_13:9780976401308
ISBN_10:0976401304
Subject: Mathematics

Convex Optimization

جزئیات و درخواست

By Stephen P. Boyd, Lieven Vandenberghe
Publisher: Cambridge University Press, 2004-03-08
Pages: 744
Language: en
ISBN_10:0521833787
ISBN_13:9780521833783
Subject: Business & Economics

Robust Equity Portfolio Management

Formulations, Implementations, and Properties using MATLAB

جزئیات و درخواست

By Woo Chang Kim, Jang Ho Kim, Frank J. Fabozzi
Publisher: John Wiley & Sons, 2015-11-25
Pages: 256
Language: en
ISBN_13:9781118797372
ISBN_10:111879737X
Subject: Business & Economics

Handbook of Semidefinite Programming

Theory, Algorithms, and Applications

جزئیات و درخواست

By Henry Wolkowicz, Romesh Saigal, Lieven Vandenberghe
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 660
Language: en
ISBN_13:9781461543817
ISBN_10:1461543819
Subject: Business & Economics

Grundlagen der praktischen Information und Dokumentation

Handbuch zur Einführung in die Informationswissenschaft und ...

جزئیات و درخواست

By Rainer Kuhlen, Wolfgang Semar, Dietmar Strauch
Publisher: Walter de Gruyter, 2013-03-22
Pages: 716
Language: de
ISBN_13:9783110258264
ISBN_10:3110258269
Subject: Language Arts & Disciplines

Arbitragetheorie und konvexe Steuern

جزئیات و درخواست

By Marcus Becker
Publisher: BoD – Books on Demand, 2017-01-31
Pages: 205
Language: de
ISBN_13:9783743193024
ISBN_10:3743193027
Subject: Business & Economics

Combinatorial and Algorithmic Mathematics

From Foundation to Optimization

جزئیات و درخواست

By Baha Alzalg
Publisher: John Wiley & Sons, 2024-10-21
Pages: 533
Language: en
ISBN_13:9781394235940
ISBN_10:1394235941
Subject: Technology & Engineering

Fighter Aircraft Maneuver Limiting Using MPC: Theory and Application

جزئیات و درخواست

By Daniel Simon
Publisher: Linköping University Electronic Press, 2017-09-12
Pages: 204
Language: en
ISBN_13:9789176854501
ISBN_10:9176854507

Deep Learning in Science

جزئیات و درخواست

By Pierre Baldi
Publisher: Cambridge University Press, 2021-07
Pages: 387
Language: en
ISBN_13:9781108845359
ISBN_10:1108845355
Subject: Computers

Analysis, Design, and Optimization of Embedded Control Systems

جزئیات و درخواست

By Amir Aminifar
Publisher: Linköping University Electronic Press, 2016-02-18
Pages: 155
Language: en
ISBN_13:9789176858264
ISBN_10:917685826X
Subject: Control systems

Exploiting Environment Configurability in Reinforcement Learning

جزئیات و درخواست

By A.M. Metelli
Publisher: IOS Press, 2022-12-07
Pages: 377
Language: en
ISBN_13:9781643683638
ISBN_10:1643683632
Subject: Computers

Machine Learning and Security

Protecting Systems with Data and Algorithms

جزئیات و درخواست

By Clarence Chio, David Freeman
Publisher: "O'Reilly Media, Inc.", 2018-01-26
Pages: 394
Language: en
ISBN_13:9781491979853
ISBN_10:1491979852
Subject: Computers

A Panorama of Mathematics: Pure and Applied

$This volume contains the proceedings of the Conference on Mathematics and its Applications-2014, held from November 14-17, 2014, at Kuwait University, Safat, Kuwait. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpufThis volume contains the proceedings of the Conference on Mathematics and its Applications–2014, held from November 14–17, 2014, at Kuwait University, Safat, Kuwait. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpuf$

جزئیات و درخواست

By Carlos M. da Fonseca, Dinh Van Huynh, Steve Kirkland, Vu Kim Tuan
Publisher: American Mathematical Soc., 2016-02-26
Pages: 292
Language: en
ISBN_13:9781470416683
ISBN_10:1470416689
Subject: Mathematics

Data-Driven Science and Engineering

Machine Learning, Dynamical Systems, and Control

جزئیات و درخواست

By Steven L. Brunton, J. Nathan Kutz
Publisher: Cambridge University Press, 2019-02-28
Pages: 495
Language: en
ISBN_13:9781108386586
ISBN_10:110838658X
Subject: Computers

Optimization and Its Applications in Control and Data Sciences

In Honor of Boris T. Polyak’s 80th Birthday

جزئیات و درخواست

By Boris Goldengorin
Publisher: Springer, 2016-09-29
Pages: 516
Language: en
ISBN_13:9783319420561
ISBN_10:3319420569
Subject: Mathematics

Inference and Learning from Data

Inference

جزئیات و درخواست

By Ali H. Sayed
Publisher: Cambridge University Press, 2022-11-30
Pages: 1165
Language: en
ISBN_13:9781009218269
ISBN_10:1009218263
Subject: Computers

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