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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 dimensionreduction to accelerate convergence of model-based optimization strategies. Thedimension-reducing subspace is updated as the trust region moves through thefunction domain, allowing OMoRF to be applied to functions with no known globallow-dimensional structure. Furthermore, its low computational requirementallows it to make rapid progress when optimizing high-dimensional functions.Its performance is examined on a set of test problems of moderate to highdimension and a high-dimensional design optimization problem. The results showthat OMoRF compares favourably to other common derivative-free optimizationmethods, even for functions in which no underlying global low-dimensionalstructure is known.

Optimization by moving ridge functions: Derivative-free optimization for computationally intensive functions