global optimization

global optimization

Lipschitz global optimization

organized by Yaroslav D. Sergeyev, Ph.D., D.Sc., D.H.C.

Global optimization is a thriving branch of applied mathematics and an extensive literature is dedicated to it (see e.g., [1–24]). In this lecture, the global optimization problem of a multidimensional function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. It is supposed that the objective function can be “black box”, multiextremal, and non-differentiable. It is also assumed that evaluation of the objective function at a point is a time-consuming operation. Many algorithms for solving this problem have been discussed in literature. They can be distinguished, for example, by the way of obtaining information about the Lipschitz constant and by the strategy of exploration of the search domain. Different exploration techniques based on various adaptive partition strategies are analyzed.

   
 
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