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**Introduction to global optimization.**
*(English)*
Zbl 0836.90134

Nonconvex Optimization and Its Applications. 3. Dordrecht: Kluwer Academic Publishers. xii, 318 (1995).

Global optimization problems where a global optimal solution and not a local one has to be sought, are more and more encountered in the modeling of real world problems. Aim of this book written by well-known researchers in the field of optimization, is to provide an introduction to specific but important classes of optimization problems. That is accomplished both by giving the fundamental theoretical results and solution algorithms.

In Chapter 1 the fundamental results on convexity and optimization are provided. Quadratic programming, concave minimization, optimization of the difference of two convex functions, Lipschitz optimization and global optimization on networks are treated in Chapters 2 to 5, respectively. Each chapter contains examples and exercises whose solutions are given at the end of the book. It is to appreciate the complexity analysis carried out for the problems investigated, the one for local minimization is not usually given in books. To sum up, the prerequisites for the book are rather modest and the book can serve as an excellent introduction to a large variety of global optimization problems.

In Chapter 1 the fundamental results on convexity and optimization are provided. Quadratic programming, concave minimization, optimization of the difference of two convex functions, Lipschitz optimization and global optimization on networks are treated in Chapters 2 to 5, respectively. Each chapter contains examples and exercises whose solutions are given at the end of the book. It is to appreciate the complexity analysis carried out for the problems investigated, the one for local minimization is not usually given in books. To sum up, the prerequisites for the book are rather modest and the book can serve as an excellent introduction to a large variety of global optimization problems.

Reviewer: M.Gaviano (Cagliari)