Connectedness and Necessary Conditions for an Extremum is popular PDF and ePub book, written by Alexey Abramov in 2013-03-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Connectedness and Necessary Conditions for an Extremum can be Read Online from any device for your convenience.
Connectedness and Necessary Conditions for an Extremum Book PDF Summary
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.
Detail Book of Connectedness and Necessary Conditions for an Extremum PDF
- Author : Alexey Abramov
- Release : 09 March 2013
- Publisher : Springer Science & Business Media
- ISBN : 9789401591195
- Genre : Mathematics
- Total Page : 213 pages
- Language : English
- PDF File Size : 11,7 Mb
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