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**Convexity and optimization in Banach spaces. 2nd rev. and extended ed. Transl. from the Romanian.**
*(English)*
Zbl 0594.49001

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.

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.

Reviewer: K.Chandrasekhara Rao

### MSC:

49-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control |

49J27 | Existence theories for problems in abstract spaces |

49K27 | Optimality conditions for problems in abstract spaces |

46A55 | Convex sets in topological linear spaces; Choquet theory |

49J40 | Variational inequalities |

49J45 | Methods involving semicontinuity and convergence; relaxation |

49N15 | Duality theory (optimization) |

49K35 | Optimality conditions for minimax problems |

90C25 | Convex programming |

93C25 | Control/observation systems in abstract spaces |

47H05 | Monotone operators and generalizations |

49J35 | Existence of solutions for minimax problems |