Titlebook: Global Optimization; Deterministic Approa Reiner Horst,Hoang Tuy Book 19901st edition Springer-Verlag Berlin Heidelberg 1990 Decision Theor

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Successive Partition MethodsThis chapter is devoted to a class of methods for concave minimization which investigate the feasible domain by dividing it into smaller pieces and refining the partition as needed (successive partition methods, branch and bound).

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Stephen A. Krawetz,David D. Wombleart involving most of the variables of the problem, and a concave part involving only a relatively small number of variables. More precisely, these problems have the form.where f: ?. → ? is a concave function, Ω is a polyhedron, d and y are vectors in ?., and n is generally much smaller than h.

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Some Important Classes of Global Optimization Problemsgramming, and Lipschitz optimization. Some basic properties of these problems and various applications are discussed. It is also shown that very general systems of equalities and (or) inequalities can be formulated as global optimization problems.

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em 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.978-3-662-02598-7

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Concavity Cutsrned with using cuts in a “.” manner: typically, cuts were generated in such a way that no feasible point of the problem is excluded and the intersection of all the cuts contains the whole feasible region. This technique is most successful when the feasible region is a convex set, so that supporting