Jaroslav M. Fowkes

Branching and Bounding Improvements for Global Optimization Algorithms with Lipschitz Continuity Properties

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Jaroslav M. Fowkes
    • Categories Global Optimization, Nonlinear Optimization Tags ,

    We present improvements to branch and bound techniques for globally optimizing functions with Lipschitz continuity properties by developing novel bounding procedures and parallelisation strategies. The bounding procedures involve nonconvex quadratic or cubic lower bounds on the objective and use estimates of the spectrum of the Hessian or derivative tensor, respectively. As the nonconvex lower bounds … Read more

    A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

  • Chris Farmer
  • Nicholas I. M. Gould
  • Jaroslav M. Fowkes
    • Categories Global Optimization Tags , ,

    We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other … Read more