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If you would like to join the seminar and are not currently affiliated with ANU, please contact Kenneth Duru at kenneth.duru@anu.edu.au.

In this talk we discuss the worst-case complexity of a wide class of non-monotone line search methods for non-convex unconstrained minimisation problems. For the algorithms in this class, the non-monotonicity is controlled by a sequence of nonnegative parameters. We prove complexity bounds to achieve approximate first-order optimality even when this sequence is not summable. As a by-product, we obtain a unified global convergence result. Our generalized results allow more freedom for the development of new non-monotone line search algorithms. As an example, we design a non-monotone scheme related to the Metropolis rule. Preliminary numerical experiments suggest that the new method is suitable to non-convex problems with many non-global local minimisers. 

This is a joint work with Ekkehard W. Sachs (University of Trier)