Global Optimization : Deterministic Approaches

The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years ago would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro­ perties. Aside from a coherent view of the field much new material is presented. By definition, a multiextremal global optimization problem seeks at least one global minimizer of a real-valued objective function that possesses different local n minimizers. The feasible set of points in IR is usually determined by a system of inequalities. It is well known that in practically all disciplines where mathematical models are used there are many real-world problems which can be formulated as multi extremal global optimization problems. Front Matter....Pages I-XIV Front Matter....Pages 1-1 Some Important Classes of Global Optimization Problems....Pages 3-50 Outer Approximation....Pages 51-84 Concavity Cuts....Pages 85-110 Branch and Bound....Pages 111-172 Front Matter....Pages 173-173 Cutting Methods....Pages 175-218 Successive Approximation Methods....Pages 219-285 Successive Partition Methods....Pages 286-370 Decomposition of Large Scale Problems....Pages 371-433 Special Problems of Concave Minimization....Pages 434-501 Front Matter....Pages 503-503 D.C. Programming....Pages 505-586 Lipschitz and Continuous Optimization....Pages 587-655 Back Matter....Pages 657-696