15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

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In memory of Christodoulos A. Floudas: Global Optimisation

14 juil. 2017 10h30 – 11h45

Salle: Amphithéâtre Banque Nationale

Présidée par Ruth Misener

3 présentations

  • 10h30 - 10h55

    Efficient calculation of spectral bounds for Hessian matrices on hyperrectangles for deterministic global optimization

    • Martin Mönnigmann, prés., Ruhr-Universität Bochum
    • Moritz Schulze Darup, Ruhr-Universität Bochum

    This presentation summarizes progress made over the past few years in the calculation of spectral bounds of interval Hessian matrices or, more generally, Hessian matrix sets for functions defined on hyperrectangles. Spectral bounds of this type play an important role in deterministic global optimization, specifically in alphaBB, an approach Professor Christodoulos A. Floudas proposed as a young researcher and continuously refined over his entire career. The presented approach deliberately avoids the computation of interval Hessian matrices. As a consequence, the method has a favorable computational complexity compared to classical approaches that do use interval Hessians. More importantly, the resulting spectral bounds are sometimes (but not in general) tighter than the tightest possible bounds that could be computed with the corresponding interval Hessian matrix.

  • 10h55 - 11h20

    Higher Order methods for solving systems of equations and for in global optimization

    • Hermann Schichl, prés., University of Vienna
    • Mihaly Csaba Markot, University of Vienna
    • Bettina Ponleitner, University of Vienna

    Professor Christodoulos A. Floudas twenty years ago proposed a method for solving
    systems of equations via a global optimization approach.
    Underdetermined systems of equations and global optimization problems with a
    submanifold of solutions often pose problems for deterministic algorithms because
    the branch-and-bound approach in this sitation usually suffers heavily from the
    cluster effect, excessive subdivision of boxes close to the solution manifold.
    In this lecture we will develop new methods to deal with solution manifolds,
    including verified computing on compact matrix Lie groups to deal with continuous
    symmetries, and a verified continuation method computing inclusion/exclusion areas
    around the solution manifold.

  • 11h20 - 11h45

    Parallel branching algorithms for the deterministic global optimisation of general NLP problems.

    • Nikolaos Kazazakis, prés., Imperial College London
    • Adjiman Claire, Imperial College London

    Deterministic global optimisation (DGO) of general NLP problems is a well-known NP-hard problem. Despite remarkable algorithmic advances in the past decades, DGO algorithms for NLP problems are not designed to take advantage of modern multiprocessor hardware, unlike their mixed-integer counterparts. In this work, we propose the first set of parallel branching algorithms for continuous NLP problems, synchronous and asynchronous versions of which are implemented in our DGO software written in C++14 and MPI-3, originally based on the MINOTAUR framework. This implementation is used to investigate the challenges which must be overcome in order to achieve linear parallel scaling.