Get this from a library connectedness and necessary conditions for an extremum a p abramov this monograph is the first book in the study of necessary conditions of an extremum in which topological connectedness plays a major role many new and original results are presented here the . 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 its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. 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. Chapter 1 necessary conditions for an extremum in this chapter we prove necessary conditions for an extremum in three basic classes of extremal problems we shall see that these conditions are formulated entirely in accordance with the lagrange principle presented in the introduction the material of this chapter is based on 0002 and 03 11
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