  A novel derivative-free algorithm, optimization by moving ridge functions
(OMoRF), for unconstrained and bound-constrained optimization is presented.
This algorithm couples trust region methodologies with output-based dimension
reduction to accelerate convergence of model-based optimization strategies. The
dimension-reducing subspace is updated as the trust region moves through the
function domain, allowing OMoRF to be applied to functions with no known global
low-dimensional structure. Furthermore, its low computational requirement
allows it to make rapid progress when optimizing high-dimensional functions.
Its performance is examined on a set of test problems of moderate to high
dimension and a high-dimensional design optimization problem. The results show
that OMoRF compares favourably to other common derivative-free optimization
methods, even for functions in which no underlying global low-dimensional
structure is known.
