Quasiconvex Optimization And Location Theory
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Quasiconvex Optimization And Location Theory
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Author : J. A. dos Santos Gromicho
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-31
Quasiconvex Optimization And Location Theory written by J. A. dos Santos Gromicho 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 1998-01-31 with Mathematics categories.
grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.
Quasiconvex Optimization And Location Theory
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Author : Joaquim A. dos Gromicho
language : en
Publisher: Thesis Pub
Release Date : 1995
Quasiconvex Optimization And Location Theory written by Joaquim A. dos Gromicho and has been published by Thesis Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Convex functions categories.
Hierarchical Optimization And Mathematical Physics
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Author : Vladimir Tsurkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
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 2013-11-21 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.
Elements For A Theory Of Decision In Uncertainty
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Author : Jaime Gil-Aluja
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements For A Theory Of Decision In Uncertainty written by Jaime Gil-Aluja 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 Business & Economics categories.
Decisions in uncertainty Scientific reaction to change During latter decades, the basic elements that have traditionally made up the society in wh ich economic activity develops, have been submitted to the effect of multiple aggressions as a consequence of the outcome of events motivated by the nature itself of the human being, always seeking a level of happiness that is never reached. In a very brief manner we are accustomed to mention these by using words such as revolution, profound changes, convulsions . . . . , the results of which are manifest through non-linear reactions that lead to a future charged with uncertainty. To get to know, explain and treat this new world constitutes one of the many objectives of those who desire a society in the service of man, and for those who aspire to the fact of the concept of mutuality transcending the use less limits of the printed word. But for this it will be necessary to overcome a whole realm of obstacles placed in the way by those comfortably embedded in old principles, decrepit ideas and are not willing to open the windows of their mind to receive the fresh air of a new era.
A Mathematical Theory Of Design Foundations Algorithms And Applications
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Author : D. Braha
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Mathematical Theory Of Design Foundations Algorithms And Applications written by D. Braha 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 Technology & Engineering categories.
Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.
Totally Convex Functions For Fixed Points Computation And Infinite Dimensional Optimization
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Author : D. Butnariu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Totally Convex Functions For Fixed Points Computation And Infinite Dimensional Optimization written by D. Butnariu 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 2012-12-06 with Mathematics categories.
The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive.
Scheduling Control Based Theory And Polynomial Time Algorithms
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Author : K. Kogan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Scheduling Control Based Theory And Polynomial Time Algorithms written by K. Kogan 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 2013-11-27 with Business & Economics categories.
This book presents a first attempt to systematically collect, classify and solve various continuous-time scheduling problems. The classes of problems distinguish scheduling by the number of machines and products, production constraints and performance measures. Although such classes are usually considered to be a prerogative of only combinatorial scheduling literature, the scheduling methodology suggested in this book is based on two mathematical tools - optimal control and combinatorics. Generally considered as belonging to two totally different areas of research and application, these seemingly irreconcilable tools can be integrated in a unique solution approach with the advantages of both. This new approach provides the possibility of developing effective polynomial-time algorithms to solve the generic scheduling problems. This book is aimed at a student audience - final year undergraduates as well as master and Ph.D. students, primarily in Operations Research, Management, Industrial Engineering and Control Systems. Indeed, some of the material in the book has formed part of the content of undergraduate and graduate courses taught at the Industrial Engineering Department of Tel-Aviv University, the Logistics Department of Bar-Ilan University and the Technology Management Department of Rolon Center for Technological Education, Israel. The book is also useful for practicing engineers interested in planning, scheduling and optimization methods. Since the book addresses the theory and design of computer-based scheduling algorithms, applied mathematicians and computer software specialists engaged in developing scheduling software for industrial engineering and management problems will find that the methods developed here can be embedded very efficiently in large applications.
Filter Design With Time Domain Mask Constraints Theory And Applications
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Author : Ba-Ngu Vo
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-31
Filter Design With Time Domain Mask Constraints Theory And Applications written by Ba-Ngu Vo 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 2001-10-31 with Computers categories.
Optimum envelope-constrained filter design is concerned with time-domain synthesis of a filter such that its response to a specific input signal stays within prescribed upper and lower bounds, while minimizing the impact of input noise on the filter output or the impact of the shaped signal on other systems depending on the application. In many practical applications, such as in TV channel equalization, digital transmission, and pulse compression applied to radar, sonar and detection, the soft least square approach, which attempts to match the output waveform with a specific desired pulse, is not the most suitable one. Instead, it becomes necessary to ensure that the response stays within the hard envelope constraints defined by a set of continuous inequality constraints. The main advantage of using the hard envelope-constrained filter formulation is that it admits a whole set of allowable outputs. From this set one can then choose the one which results in the minimization of a cost function appropriate to the application at hand. The signal shaping problems so formulated are semi-infinite optimization problems. This monograph presents in a unified manner results that have been generated over the past several years and are scattered in the research literature. The material covered in the monograph includes problem formulation, numerical optimization algorithms, filter robustness issues and practical examples of the application of envelope constrained filter design. Audience: Postgraduate students, researchers in optimization and telecommunications engineering, and applied mathematicians.
Nonlinear Optimization And Related Topics
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Author : Gianni Pillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Nonlinear Optimization And Related Topics written by Gianni Pillo 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.
This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.
Managing In Uncertainty Theory And Practice
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Author : Constantin Zopounidis
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-31
Managing In Uncertainty Theory And Practice written by Constantin Zopounidis 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 1998-08-31 with Business & Economics categories.
This book provides a new point of view on the subject of the management of uncertainty. It covers a wide variety of both theoretical and practical issues involving the analysis and management of uncertainty in the fields of finance, management and marketing. Audience: Researchers and professionals from operations research, management science and economics.