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Titlebook: Connectedness and Necessary Conditions for an Extremum; Alexander P. Abramov Book 1998 Springer Science+Business Media B.V. 1998 Euler–Lag

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发表于 2025-3-21 17:29:47 | 显示全部楼层 |阅读模式
书目名称Connectedness and Necessary Conditions for an Extremum
编辑Alexander P. Abramov
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Connectedness and Necessary Conditions for an Extremum;  Alexander P. Abramov Book 1998 Springer Science+Business Media B.V. 1998 Euler–Lag
描述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 trivia
出版日期Book 1998
关键词Euler–Lagrange equation; Optimal control; functional analysis; linear optimization; nonlinear optimizati
版次1
doihttps://doi.org/10.1007/978-94-015-9119-5
isbn_softcover978-90-481-4981-0
isbn_ebook978-94-015-9119-5
copyrightSpringer Science+Business Media B.V. 1998
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发表于 2025-3-21 22:13:24 | 显示全部楼层
Alternative Conditions for an Extremum of the First Order, ... , .. and on some neighborhood of a point . ∈ .. Let us assume that the functional . has a local minimum on . at the point .. The Dubovitskĭ-Milyutin approach of the analysis of necessary conditions for an extremum presupposes that the sets Si, . = 1, ... , . − 1, have internal points, but the s
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Necessary Conditions for an Extremum in a Measure Space,ar and topological structures there is also a measure, i.e., some .-algebra Σ of its subsets and a full measure . on Σ are given in . [Hal, KA, KoF]. Here we assume that the topology in . is induced by some metric. Thus in this chapter the space . is a complete metrizable locally convex linear topol
发表于 2025-3-22 09:01:35 | 显示全部楼层
tions 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
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https://doi.org/10.1007/978-3-662-29644-8et .. has no such points. As a rule, the sets .., ... , .. are defined by some inequalities, and .. is defined by some system of equalities. We recall some definitions and results of this approach [Gir, DuM1, DuM2].
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Book 1998an 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. Rega
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