Mathematics of Optimization: Smooth and Nonsmooth Case - by Giorgio Giorgi & A Guerraggio & J Thierfelder (Hardcover)

Book Synopsis

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.

Review Quotes

"To the reader who seeks a comprehensive, rigorous text on optimization in a finite dimensional space, with detailed, clear explanations and examples, the book could be very acttractive." --Zvi Artstein (Rehovot), in: Mathematical Reviews, 2005

"The book contains several excellent tables and figures which summarize interrelations between different concepts, like different notions of convexity, or the implications between the numerous constraint quailifications." --Mirjam Dür (Darmstadt University of Technology), in: Mathematical Methods of Operational Research, p.2, Vol. 61, 2005)