Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
On the Global Convergence of Derivative-Free Methods for Unconstrained Optimization
SIAM Journal on Optimization
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Multidirectional search: a direct search algorithm for parallel machines
Multidirectional search: a direct search algorithm for parallel machines
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
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Direct search methods have been an area of active research in recent years. On many real-world problems involving computationally expensive and often noisy functions, they are one of the few applicable alternatives. However, although these methods are usually easy to implement, robust and provably convergent in many cases, they suffer from a slow rate of convergence.Usually these methods do not take the local topography of the objective function into account. We present a new algorithm for unconstrained optimisation which is a modification to a basic generating set search method. The new algorithm tries to adapt its search directions to the local topography by accumulating curvature information about the objective function as the search progresses.The curvature information is accumulated over a region thus smoothing out noise and minor discontinuities. We present some theory regarding its properties, as well as numerical results. Preliminary numerical testing shows that the new algorithm outperforms the basic method most of the time, sometimes by significant relative margins, on noisy as well as smooth problems.