Connectedness And Necessary Conditions For An Extremum
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Connectedness And Necessary Conditions For An Extremum
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Author : Alexey Abramov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Connectedness And Necessary Conditions For An Extremum written by Alexey Abramov 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 Mathematics categories.
The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.
Connectedness And Necessary Conditions For An Extremum
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Author : Alexey Abramov
language : en
Publisher: Springer
Release Date : 2014-10-09
Connectedness And Necessary Conditions For An Extremum written by Alexey Abramov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-09 with Mathematics categories.
The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.
Estimators For Uncertain Dynamic Systems
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Author : A.I. Matasov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Estimators For Uncertain Dynamic Systems written by A.I. Matasov 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 Technology & Engineering categories.
When solving the control and design problems in aerospace and naval engi neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from mea surement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple mentation. For example, the dimension of these algorithms can be very high.
Geometrical Methods In Variational Problems
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Author : N.A. Bobylov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometrical Methods In Variational Problems written by N.A. Bobylov 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.
This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods. Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.
Connectedness And Necessary Conditions For An Extremum
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Author : Alexey Abramov
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-31
Connectedness And Necessary Conditions For An Extremum written by Alexey Abramov 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 1998-03-31 with Mathematics categories.
The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.
The Mechanics And Thermodynamics Of Continuous Media
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Author : Miroslav Silhavy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
The Mechanics And Thermodynamics Of Continuous Media written by Miroslav Silhavy 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 Science categories.
This book presents the nonlinear theories of continuum thermomechanics. Through out 1 emphasize issues that are foundational in nature, and seek results common to materials of arbitrary symmetry. The central part of the book deals with thermoelastic bodies with heat conduction and viscosity, including the inviscid or ideal dissipation less bodies. A surprising variety of phenomena can be modeled within this frame work. Moreover, the main ideas can be transferred into more complicated theories. At present, the major challenge to the non linear thermoelasticity is posed by phase transformations with changes in symmetry. 1. W. Gibbs' immensely inftuen tiaI treatise On the equilibrium of heterogeneous substances has provided a highly successful theory of phase transitions in ftuids. Gibbs brought the view that the ther modynamics is not only the theory of heat, but also a theory of equilibrium, with the of the book is an extension of main tool the minimum principles. A large portion Gibbs' ideas to bodies of general symmetry by the methods of the calculus of varia tions. The interplay between the convexity properties of the stored energy functions, the resulting equations, and the physics of the phenomena is a leading theme.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1999-11
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11 with Mathematics categories.
International Mathematical News
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Author :
language : en
Publisher:
Release Date : 1997
International Mathematical News written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Soviet Mathematics Doklady
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Author :
language : en
Publisher:
Release Date : 1984
Soviet Mathematics Doklady written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Smooth Nonlinear Optimization In Rn
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Author : Tamás Rapcsák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Smooth Nonlinear Optimization In Rn written by Tamás Rapcsák 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.
Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.