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تعداد نتایج: 780

Gemischt-ganzzahlige Optimierung: Modellierung in der Praxis

Mit Fallstudien aus Chemie, Energiewirtschaft, Papierindustr...

By Josef Kallrath
Publisher: Springer-Verlag, 2012-11-05
Pages: 381
Language: de
ISBN_13:9783658006907
ISBN_10:3658006900
Subject: Mathematics

Grundlagen der Mathematischen Optimierung

Diskrete Strukturen, Komplexitätstheorie, Konvexitätstheorie...

جزئیات و درخواست

By Peter Gritzmann
Publisher: Springer-Verlag, 2013-01-06
Pages: 533
Language: de
ISBN_13:9783834820112
ISBN_10:3834820113
Subject: Mathematics

A Long View of Research and Practice in Operations Research and Management Science

The Past and the Future

جزئیات و درخواست

By ManMohan S. Sodhi, Christopher S. Tang
Publisher: Springer Science & Business Media, 2010-09-09
Pages: 308
Language: en
ISBN_13:9781441968104
ISBN_10:1441968105
Subject: Business & Economics

Millions, Billions, Zillions

Defending Yourself in a World of Too Many Numbers

جزئیات و درخواست

By Brian W. Kernighan
Publisher: Princeton University Press, 2020-11-10
Pages: 176
Language: en
ISBN_13:9780691209098
ISBN_10:069120909X
Subject: Mathematics

Understanding the Digital World

What You Need to Know about Computers, the Internet, Privacy...

جزئیات و درخواست

By Brian W. Kernighan
Publisher: Princeton University Press, 2021-03-30
Pages: 301
Language: en
ISBN_13:9780691219103
ISBN_10:0691219109
Subject: Computers

Principles and Practice of Constraint Programming

24th International Conference, CP 2018, Lille, France, Augus...

جزئیات و درخواست

By John Hooker
Publisher: Springer, 2018-08-22
Pages: 777
Language: en
ISBN_13:9783319983349
ISBN_10:3319983342
Subject: Mathematics

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

Introduction to Financial Technology

جزئیات و درخواست

By Roy S. Freedman
Publisher: Elsevier, 2006-04-24
Pages: 365
Language: en
ISBN_13:9780080461847
ISBN_10:0080461840
Subject: Business & Economics

Mixed Integer Nonlinear Programming

جزئیات و درخواست

By Jon Lee, Sven Leyffer
Publisher: Springer Science & Business Media, 2011-12-02
Pages: 687
Language: en
ISBN_13:9781461419273
ISBN_10:1461419271
Subject: Mathematics

Food Engineering Interfaces

جزئیات و درخواست

By José Miguel Aguilera, Ricardo Simpson, Jorge Welti-Chanes, Daniela Bermudez Aguirre, Gustavo Barbosa-Canovas
Publisher: Springer Science & Business Media, 2010-12-25
Pages: 700
Language: en
ISBN_13:9781441974754
ISBN_10:144197475X
Subject: Technology & Engineering

Optimal Operation and Control of Power Systems Using an Algebraic Modelling Language

جزئیات و درخواست

By Nnamdi Nwulu, Saheed Lekan Gbadamosi
Publisher: Springer Nature, 2021-01-04
Pages: 264
Language: en
ISBN_13:9783030003951
ISBN_10:3030003957
Subject: Technology & Engineering

Computational Modeling and Problem Solving in the Networked World

Interfaces in Computer Science and Operations Research

جزئیات و درخواست

By Hemant K. Bhargava, Nong Ye
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 322
Language: en
ISBN_13:9781461510437
ISBN_10:1461510430
Subject: Computers

An Enduring Quest

The Story Of Purdue Industrial Engineers

جزئیات و درخواست

By Ferd Leimkuhler
Publisher: Purdue University Press, 2019-07-15
Pages: 302
Language: en
ISBN_13:9781557539182
ISBN_10:1557539189
Subject: Technology & Engineering

Numerical Software with Result Verification

International Dagstuhl Seminar, Dagstuhl Castle, Germany, Ja...

جزئیات و درخواست

By René Alt, Andreas Frommer, R. Baker Kearfott, Wolfram Luther
Publisher: Springer, 2004-02-12
Pages: 324
Language: en
ISBN_13:9783540247388
ISBN_10:3540247386
Subject: Computers

Proceedings of the EWG-DSS Liverpool-2012 Workshop

Decision Support Systems & Operations Management Trends and ...

جزئیات و درخواست

By F. Dargam, B. Delibašić, J.E. Hernández, S. Liu, R. Ribeiro
Publisher: EWG-DSS, 2012-04-12
Pages: 157
Language: en
ISBN_13:9780956112248
ISBN_10:0956112242
Subject: Business & Economics

Modeling Languages in Mathematical Optimization

جزئیات و درخواست

By Josef Kallrath
Publisher: Springer Science & Business Media, 2013-12-01
Pages: 427
Language: en
ISBN_13:9781461302155
ISBN_10:1461302153
Subject: Mathematics

Computing Tools for Modeling, Optimization and Simulation

Interfaces in Computer Science and Operations Research

جزئیات و درخواست

By Manuel Laguna, José Luis González-Velarde
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 318
Language: en
ISBN_13:9781461545675
ISBN_10:1461545676
Subject: Business & Economics

Algorithms for Continuous Optimization

The State of the Art

جزئیات و درخواست

By E. Spedicato
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 572
Language: en
ISBN_13:9789400903692
ISBN_10:9400903693
Subject: Mathematics

Algebraic Modeling Systems

Modeling and Solving Real World Optimization Problems

جزئیات و درخواست

By Josef Kallrath
Publisher: Springer Science & Business Media, 2012-02-14
Pages: 255
Language: en
ISBN_13:9783642235924
ISBN_10:3642235921
Subject: Business & Economics

Operations Research and Cyber-Infrastructure

جزئیات و درخواست

By John W. Chinneck, Bjarni Kristjansson, Matthew J. Saltzman
Publisher: Springer Science & Business Media, 2009-01-05
Pages: 460
Language: en
ISBN_13:9780387888439
ISBN_10:0387888438
Subject: Computers

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