Lipschitz continuity and the termination of interval methods for global optimization

AbstractIn this paper, it is shown how the Lipschitz continuity of a global optimization problem's objective function influences the termination of a Hansen type method. The results concern applying different termination criteria to a Hansen method and retrieving more information than explicitly supplied by a certain criterion. A similar result for Moore-Skelboe methods arises, as a consequence

A methodology of parallelization for continuous verified global optimization

International audienceHansen's algorithm for verified continuous global optimization is based on interval arithmetic. It is of the Branch&Bound type. Our proposal for the parallelization of Hansen's algorithm consists in creating a lightweight process or thread to explore each subinterval and in beginning its execution immediately after its creation. This strategy provides a high level of speculation and enables to virtualize the architecture. The implementation of this parallel algorithm is based on the parallel execution support PM2 for the handling of threads at a low cost and on the PROFIL/BIAS interval library. Preliminary experimental results exhibit superlinear speed-ups

A metaheuristic methodology based on the limitation of the memory of interval branch and bound algorithms

Interval analysis, Branch and bound, Limited memory, Metaheuristic, Algorithmic complexity,