Includes bibliographical references (p. 773-793) and index.

Hector O. Fattorini's Infinite Dimensional Optimization and Control Theory provides a comprehensive exploration of optimal control problems for systems described by ordinary and partial differential equations. The book delves into the theoretical foundations of these problems, offering a unified framework that bridges the gap between finite and infinite dimensional control theory. Key topics include the existence and necessary conditions for optimal control, derived from Kuhn-Tucker theorems in infinite dimensional spaces. The author employs various mathematical tools to study evolution partial differential equations, leading to a general theory of relaxed controls that ensures the existence of optimal controls for arbitrary control sets. The book's applications encompass nonlinear systems described by partial differential equations of hyperbolic and parabolic type, and it provides valuable insights into the convergence of suboptimal controls. Overall, Infinite Dimensional Optimization and Control Theory offers a deep and insightful exploration of the theoretical and practical aspects of optimal control in infinite dimensional spaces, making it a valuable resource for researchers, students, and practitioners in the field of control theory.