Author: Roberto Lucchetti
Publisher: Springer Science & Business Media
ISBN: 9401584729
Category : Mathematics
Languages : en
Pages : 271
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Book Description
This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.
Author: Qamrul Hasan Ansari
Publisher: Springer Science & Business Media
ISBN: 3642211143
Category : Business & Economics
Languages : en
Pages : 568
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Book Description
We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.
Author: David E. Stewart
Publisher: SIAM
ISBN: 9781611970715
Category : Science
Languages : en
Pages : 400
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Book Description
This book addresses dynamics with inequalities comprehensively. The author develops the theory and application of dynamical systems that incorporate some kind of hard inequality constraint, such as mechanical systems with impact; electrical circuits with diodes (as diodes permit current flow in only one direction); and social and economic systems that involve natural or imposed limits (such as traffic flow, which can never be negative, or inventory, which must be stored within a given facility). This book demonstrates that hard limits - eschewed in most dynamical models - are natural models for many dynamic phenomena, and there are ways of creating differential equations with hard constraints that provide accurate models of many physical, biological, and economic systems. The author discusses how finite- and infinite-dimensional problems are treated in a unified way so the theory is applicable to both ordinary differential equations and partial differential equations.
Author: Nira Dyn
Publisher: World Scientific
ISBN: 1783263040
Category : Mathematics
Languages : en
Pages : 168
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Book Description
This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
Author: E.W. Sachs
Publisher: Springer
ISBN: 0387356991
Category : Technology & Engineering
Languages : en
Pages : 334
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Book Description
System Modeling and Optimization XX deals with new developments in the areas of optimization, optimal control and system modeling. The themes range across various areas of optimization: continuous and discrete, numerical and analytical, finite and infinite dimensional, deterministic and stochastic, static and dynamic, theory and applications, foundations and case studies. Besides some classical topics, modern areas are also presented in the contributions, including robust optimization, filter methods, optimization of power networks, data mining and risk control. This volume contains invited and selected papers from presentations at the 20th IFIP TC7 Conference on System Modeling and Optimization, which took place at the University of Trier, Germany from July 23 to 27, 2001, and which was sponsored by the International Federation for Information Processing (IFIP).
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 844
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Book Description
Author: Luciano Carbone
Publisher: CRC Press
ISBN: 9781420035582
Category : Mathematics
Languages : en
Pages : 414
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Book Description
Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener
Author: Alexander Ioffe
Publisher: CRC Press
ISBN: 100065740X
Category : Mathematics
Languages : en
Pages : 278
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Book Description
The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Author: Giuseppe Buttazzo
Publisher: Oxford University Press
ISBN: 9780198504658
Category : Mathematics
Languages : en
Pages : 282
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Book Description
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Author: F. Giannessi
Publisher: Springer Science & Business Media
ISBN: 0306480263
Category : Mathematics
Languages : en
Pages : 304
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Book Description
The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.
