Introduction to Global Optimization
Springer Science & Business Media, 30 thg 6, 1995 - 320 trang
Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications.
Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved.
Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering.
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algorithm applied approach approximation assume attained branch and bound called Chapter Choose closed Compute concave concave function cone Consider constant constraints construct containing continuous convex envelope convex functions convex set corresponding cost defined definition denote determined direction discussed edge equivalent example Exercise exists extreme feasible feasible point finite flow formulation function f given global global minimum global optimization hence holds hyperplane implies inequality initial integer intersection iteration known linear program Lipschitz lower bound matrix maximum method Moreover node Note objective function obtain optimal solution optimization problem partition polytope positive problem procedure programming problem Proof Proposition Prove quadratic rectangle respectively result satisfying sequence simplex solution solving Theorem upper bound variables vector vertex vertices xTQx yields
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