### Jaroslav Fowkes (University of Edinburgh)

#### Global optimization of Lipschitz continuous functions

*Wednesday 5 October 2011 at 14.30, JCMB 6206*

##### Abstract

This talk will consist of two parts. In the first part we will present a
motivating application from oil reservoir simulation, namely finding the
location and trajectory of an oil producing well which maximises oil
production. We will show how such a problem can be tackled through the use of
radial basis function (RBF) approximation (also known as Kriging or Gaussian
process regression) and a branch and bound global optimization algorithm.

In the second part of the talk we will show how one can improve the branch and
bound algorithm through the use of Lipschitz continuity of the RBF
approximation. This leads to an entirely new global optimization algorithm for
twice differentiable functions with Lipschitz continuous Hessian. The
algorithm makes use of recent cubic regularisation techniques from local
optimization to obtain the necessary bounds within the branch and bound
algorithm.

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