Hierarchical Optimization And Mathematical Physics
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Hierarchical Optimization And Mathematical Physics
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Author : Vladimir Tsurkov
language : en
Publisher: Springer
Release Date : 2013-11-15
Hierarchical Optimization And Mathematical Physics written by Vladimir Tsurkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-15 with Science categories.
This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problern with macrovariables, whose number is less than the number of initial variables. This problern is often very simple. On the lower level, we have the usual optimal control problems of math ematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems ofless dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problern and converge to its optimal solutionunder certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assem bles the final production from the components produced by the subsystems.
Hierarchical Optimization And Mathematical Physics
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Author : Vladimir Tsurkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-31
Hierarchical Optimization And Mathematical Physics written by Vladimir Tsurkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-31 with Science categories.
This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problern with macrovariables, whose number is less than the number of initial variables. This problern is often very simple. On the lower level, we have the usual optimal control problems of math ematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems ofless dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problern and converge to its optimal solutionunder certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assem bles the final production from the components produced by the subsystems.
Large Scale Optimization
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Author : Vladimir Tsurkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Large Scale Optimization written by Vladimir Tsurkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.
Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.
Optimization Theory
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Author : F. Giannessi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Optimization Theory written by F. Giannessi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu able comments. Special thanks are directed to our sponsors, the Hun garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.
Aggregation In Large Scale Optimization
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Author : I. Litvinchev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Aggregation In Large Scale Optimization written by I. Litvinchev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
When analyzing systems with a large number of parameters, the dimen sion of the original system may present insurmountable difficulties for the analysis. It may then be convenient to reformulate the original system in terms of substantially fewer aggregated variables, or macrovariables. In other words, an original system with an n-dimensional vector of states is reformulated as a system with a vector of dimension much less than n. The aggregated variables are either readily defined and processed, or the aggregated system may be considered as an approximate model for the orig inal system. In the latter case, the operation of the original system can be exhaustively analyzed within the framework of the aggregated model, and one faces the problems of defining the rules for introducing macrovariables, specifying loss of information and accuracy, recovering original variables from aggregates, etc. We consider also in detail the so-called iterative aggregation approach. It constructs an iterative process, at· every step of which a macroproblem is solved that is simpler than the original problem because of its lower dimension. Aggregation weights are then updated, and the procedure passes to the next step. Macrovariables are commonly used in coordinating problems of hierarchical optimization.
Generalized Optimal Control Of Linear Systems With Distributed Parameters
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Author : S.I. Lyashko
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-27
Generalized Optimal Control Of Linear Systems With Distributed Parameters written by S.I. Lyashko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-27 with Mathematics categories.
The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail.
Cooperative Control And Optimization
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Author : Robert Murphey
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-31
Cooperative Control And Optimization written by Robert Murphey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-31 with Business & Economics categories.
Table of contents
Optimization And Related Topics
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Author : Alexander M. Rubinov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Optimization And Related Topics written by Alexander M. Rubinov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Computers categories.
This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: • optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. • emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. • gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. • auxiliary function, generalized penalty function, modified Lagrange func tion. • convexity, quasiconvexity, abstract convexity.
Models For Parallel And Distributed Computation
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Author : R. Correa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Models For Parallel And Distributed Computation written by R. Correa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
Parallel and distributed computation has been gaining a great lot of attention in the last decades. During this period, the advances attained in computing and communication technologies, and the reduction in the costs of those technolo gies, played a central role in the rapid growth of the interest in the use of parallel and distributed computation in a number of areas of engineering and sciences. Many actual applications have been successfully implemented in various plat forms varying from pure shared-memory to totally distributed models, passing through hybrid approaches such as distributed-shared memory architectures. Parallel and distributed computation differs from dassical sequential compu tation in some of the following major aspects: the number of processing units, independent local dock for each unit, the number of memory units, and the programming model. For representing this diversity, and depending on what level we are looking at the problem, researchers have proposed some models to abstract the main characteristics or parameters (physical components or logical mechanisms) of parallel computers. The problem of establishing a suitable model is to find a reasonable trade-off among simplicity, power of expression and universality. Then, be able to study and analyze more precisely the behavior of parallel applications.
Topics In Industrial Mathematics
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Author : H Neunzert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Topics In Industrial Mathematics written by H Neunzert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Industrial Mathematics is a relatively recent discipline. It is concerned primarily with transforming technical, organizational and economic problems posed by indus try into mathematical problems; "solving" these problems byapproximative methods of analytical and/or numerical nature; and finally reinterpreting the results in terms of the original problems. In short, industrial mathematics is modelling and scientific computing of industrial problems. Industrial mathematicians are bridge-builders: they build bridges from the field of mathematics to the practical world; to do that they need to know about both sides, the problems from the companies and ideas and methods from mathematics. As mathematicians, they have to be generalists. If you enter the world of indus try, you never know which kind of problems you will encounter, and which kind of mathematical concepts and methods you will need to solve them. Hence, to be a good "industrial mathematician" you need to know a good deal of mathematics as well as ideas already common in engineering and modern mathematics with tremen dous potential for application. Mathematical concepts like wavelets, pseudorandom numbers, inverse problems, multigrid etc., introduced during the last 20 years have recently started entering the world of real applications. Industrial mathematics consists of modelling, discretization, analysis and visu alization. To make a good model, to transform the industrial problem into a math ematical one such that you can trust the prediction of the model is no easy task.