Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, April 01, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Yves Brise

Lipschitzian Optimization, DIRECT Algorithm, and Applications

Selected from the large and diverse topic of function optimization, we will have a closer look at a direct, global search technique for minimization. In 1972 Shubert proposed an optimization algorithm for Lipschitz-continuous functions, which subsequently partitions the search space into smaller and smaller regions. The decision on which region the algorithm should recurse on is based on the Lipschitz constant of the function. This algorithm, as concise as it may be, has several major deficiencies.

In 1993, Jones, Perttunen, and Stuckman proposed a very clever adaption of Shubert's algorithm that largely alleviates those problems and that has been successfully applied to actual optimization problems. They called their algorithm DIRECT (for DIviding RECTangles). It is interestig to see that, at its heart, this algorithm is purely geometrical. It requires no knowledge of the Lipschitz constant, nor any derivative information. It only needs to be able to evaluate the function. Also note that DIRECT is a deterministic algorithm that, given enough time, gets arbitrarily close to the global optimum.

In the last years there have been a few new results and adaptions of DIRECT. As time permits we are going to see some of those results and/or some applications.

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