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تعداد نتایج: 591

Fundamentals of Convex Analysis

By Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
Publisher: Springer Science & Business Media, 2004-04-21
Pages: 278
Language: en
ISBN_10:3540422056
ISBN_13:9783540422051
Subject: Computers

Fundamentals of Convex Analysis

Duality, Separation, Representation, and Resolution

جزئیات و درخواست

By M.J. Panik
Publisher: Springer Science & Business Media, 2013-03-09
Pages: 313
Language: en
ISBN_13:9789401581240
ISBN_10:940158124X
Subject: Mathematics

Fundamentals of Convex Analysis and Optimization

A Supremum Function Approach

جزئیات و درخواست

By Rafael Correa, Abderrahim Hantoute, Marco A. López
Publisher: Springer Nature, 2023-07-11
Pages: 451
Language: en
ISBN_13:9783031295515
ISBN_10:303129551X
Subject: Business & Economics

Fundamentals of Convex Analysis

جزئیات و درخواست

By M J Panik
1993-06-30
Pages: 320
Language: en
ISBN_10:9401581258
ISBN_13:9789401581257

Convex Analysis and Minimization Algorithms

جزئیات و درخواست

By Jean-Baptiste Hiriart-Urruty
1993
Language: en
OTHER:LCCN:93006137
Subject: Convex functions

Convex Analysis

Theory and Applications

جزئیات و درخواست

By Georgii G. Magaril-Ilʹyaev, Vladimir Mikhaĭlovich Tikhomirov
Publisher: American Mathematical Soc.,
Pages: 196
Language: en
ISBN_10:0821889648
ISBN_13:9780821889640
Subject: Mathematics

Convex Analysis and Nonlinear Optimization

Theory and Examples

جزئیات و درخواست

By Jonathan Borwein, Adrian S. Lewis
Publisher: Springer Science & Business Media, 2010-05-05
Pages: 316
Language: en
ISBN_13:9780387312569
ISBN_10:0387312560
Subject: Mathematics

Theorie der konvexen Körper

جزئیات و درخواست

By T. Bonnesen, W. Fenchel
Publisher: Springer-Verlag, 2013-03-13
Pages: 177
Language: de
ISBN_13:9783642930140
ISBN_10:364293014X
Subject: Mathematics

Generatives Deep Learning

Maschinen das Malen, Schreiben und Komponieren beibringen

جزئیات و درخواست

By David Foster
Publisher: O'Reilly, 2020-03-24
Pages: 351
Language: de
ISBN_13:9783960103547
ISBN_10:3960103549
Subject: Computers

Foundations of Optimization

جزئیات و درخواست

By Osman Güler
Publisher: Springer Science & Business Media, 2010-08-03
Pages: 445
Language: en
ISBN_13:9780387684079
ISBN_10:0387684077
Subject: Business & Economics

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

Numerische Verfahren der konvexen, nichtglatten Optimierung

Eine anwendungsorientierte Einführung

جزئیات و درخواست

By Walter Alt
Publisher: Springer-Verlag, 2013-03-12
Pages: 180
Language: de
ISBN_10:3322800830
ISBN_13:9783322800831
Subject: Mathematics

Nonlinear and Mixed-Integer Optimization

Fundamentals and Applications

جزئیات و درخواست

By Christodoulos A. Floudas
Publisher: Oxford University Press, 1995-10-05
Pages: 475
Language: en
ISBN_13:9780195100563
ISBN_10:0195100565
Subject: Business & Economics

Nonsmooth Mechanics and Convex Optimization

جزئیات و درخواست

By Yoshihiro Kanno
Publisher: CRC Press, 2011-04-05
Pages: 447
Language: en
ISBN_13:9781420094237
ISBN_10:1420094238
Subject: Science

Convex Functional Analysis

جزئیات و درخواست

By Andrew J. Kurdila, Michael Zabarankin
Publisher: Springer Science & Business Media, 2006-03-30
Pages: 238
Language: en
ISBN_13:9783764373573
ISBN_10:3764373571
Subject: Science

Convex Optimization

جزئیات و درخواست

By Stephen Boyd, Lieven Vandenberghe
Publisher: Cambridge University Press, 2004-03-08
Pages: 744
Language: en
ISBN_13:9781107394001
ISBN_10:1107394007
Subject: Mathematics

Topologie und Funktionalanalysis

Grundlagen der Abstrakten Analysis mit Anwendungen

جزئیات و درخواست

By Jürgen Heine
Publisher: Walter de Gruyter, 2012-11-21
Pages: 760
Language: de
ISBN_13:9783486719680
ISBN_10:3486719688
Subject: Mathematics

Offene Quantensysteme

Die Primas Lectures

جزئیات و درخواست

By Anton Amann, Ulrich Müller-Herold
Publisher: Springer-Verlag, 2011-01-04
Pages: 246
Language: de
ISBN_13:9783642051876
ISBN_10:3642051871
Subject: Science

Decision Sciences

Theory and Practice

جزئیات و درخواست

By Raghu Nandan Sengupta, Aparna Gupta, Joydeep Dutta
Publisher: CRC Press, 2016-11-30
Pages: 936
Language: en
ISBN_13:9781351727402
ISBN_10:1351727400
Subject: Business & Economics

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

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