Essays and Surveys in Global Optimization

Charles Audet · Pierre Hansen · Giles Savard

2005年12月 · GERAD 25th anniversary series 第 7 本图书 · Springer Science & Business Media

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Global optimization aims at solving the most general problem of deterministic mathematical programming: to find the global optimum of a nonlinear, nonconvex, multivariate function of continuous and/or integer variables subject to constraints which may be themselves nonlinear and nonconvex. In addition, once the solution is found, proof of its optimality is also expected from this methodology. ESSAYS AND SURVEYS IN GLOBAL OPTIMIZATION is the most recent examination of its mathematical capability, power, and wide ranging solution to many fields in the applied sciences.

In a series of topical chapters, the first section of the book appraises the mathematical properties and algorithms for general global optimization problems. These include chapters on "Unilateral Analysis and Duality"; "Monotonic Optimization: Branch and Cut Methods"; "Duality Bound Methods in Global Optimization"; "General Quadratic Programming"; "On Solving Polynomial, Factorable, and Black-Box Optimization Problems using the RLT Methodology"; and "Bilevel Programming." The book’s second section offers a variety of current application chapters where global optimization has been applied to assorted problems in diverse fields. These include chapters on "Application of Global Optimization to Portfolio Analysis"; "Optimization Techniques in Medicine"; "Global Optimization in Geometry—Circle Packing into the Square"; and "A Deterministic Global Optimization Algorithm for Design Problems."

The topics presented in this volume, ESSAYS AND SURVEYS IN GLOBAL OPTIMIZATION, attest to the successes of researchers in the field, the power of its methods, the diversity of its applications and the variety of the ideas and research poles it explores.