Convexity and optimization in Banach spaces

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.