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Partition Algorithms on Multidimensional Intervals

  • János D. Pintér
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 6)

Abstract

The present chapter is devoted to the analysis of adaptive partition strategies to solve the multivariate global optimization problem
$$\mathop {\min }\limits_{x \in D} f(x),$$
(2.4.1)
Where
$$D = [a,b] \subset I{R^n},a = ({a_1}, \ldots ,{a_n}),b = ({b_1}, \ldots {b_n}), - \infty < {a_j} < {b_j} < \infty ,j = 1 \ldots ,n.$$
Obviously, (2.4.1) is a special case of the general GOP stated in Section 2.1.1, if we suppose the continuity or Lipschitz-continuity of f. As earlier, X* denotes the set of globally optimal solutions to (2.4.1), and z* = f(x*) for x* ∈ X*.

Keywords

Global Optimization Vertex Function Search Point Partition Strategy Partition Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • János D. Pintér
    • 1
  1. 1.Pintér Consulting ServicesDalhousie UniversityCanada

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