an:03955816
Zbl 0594.49001
Barbu, V.; Precupanu, Th.
Convexity and optimization in Banach spaces. 2nd rev. and extended ed. Transl. from the Romanian
EN
Mathematics and Its Applications (East European Series), 10. Dordrecht/Boston/Lancaster: D. Reidel Publishing Company, a member of the Kluwer Academic Publishers Group; Bucure??ti: Editura Academiei. XVII, 397 p. Dfl. 190.00; {\$} 64.00; \textsterling 52.75 (1986).
1986
b
49-01 49J27 49K27 46A55 49J40 49J45 49N15 49K35 90C25 93C25 47H05 49J35
Convexity in topological linear spaces; maximal monotone operators; evolution systems in Banach spaces; subdifferential; distributed control; boundary control; duality theory; Minimax problems
The chapter titles are: 1. Fundamentals of functional analysis; 2. Convex functions; 3. Convex programming; and 4. Convex control problems in Banach spaces.
Convexity in topological linear spaces, maximal monotone operators and evolution systems in Banach spaces, the subdifferential of a convex function, concave-convex functions, convex distributed control problems, synthesis of optimal control, boundary control problems with convex cost criteria are some of the topics discussed in this book. Applications of duality theory are also given. Minimax problems and variational inequalities appear as applications. Concepts are explained by means of illustrations. For instance, self-adjoint operators in Hilbert spaces are cited as an example of monotone operators.
Printing and get-up are attractive. This is a good text on optimization and control theory.
K.Chandrasekhara Rao
Zbl 0317.49011; Zbl 0379.49010