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It was our intention to make the book seIf-contained and accessible to a large number of readerso To achieve this in Chapter I we have summarized with or without proofs some basic results in functional analysis and non-linear operator equations in Banach spaces. The list of references is not intended to be complete. It refers only to papers which were used or are directly connected with the subjects treated in this book. V. BARBU Jassy, July 1974 TH. PRECUPANU x Pre tace to the English edition This English edition differs from the Romanian version in that several ehanges have been made. Several seetions in Chapters III and IV have been entirely rewritten and several errors and inaccuracies in the first edition were correeted. The authors wish to express their gratitude to Dr. V. Popescu, from the Jassy University, who kindly assisted them in reading various parts of the manuseript, eorreeting errors and improv ing the presentation.
List of contents
1 Fundamentals of Functional Analysis.- 1 Convexity in topological linear spaces.- 2 Duality in linear normed spaces.- 3 Vector-valued functions and distributions.- 4 Maximal monotone operators.- 2 Convex Functions.- 1 General properties of convex functions.- 2 The subdifferential of a convex function.- 3 Concave-convex functions.- Bibliographical notes.- 3 Convex Programming.- 1 Optimality conditions.- 2 Duality in convex programming.- 3 Applications of the duality theory.- Bibliographical notes.- 4 Convex Control Problems in Hilbert Spaces.- 1 Necessary and sufficient conditions for optimality.- 2 The dual optimal control problem.- 3 Convex control problems associated with linear evolutionary processes in Hilbert space.- 4 Synthesis of optimal control.- Bibliographical notes.
