A direct search method for smooth and nonsmooth unconstrained optimization

Christopher John Price, M. Reale, B. L. Robertson
2008 ANZIAM Journal  
A derivative free frame based method for minimizing C 1 and nonsmooth functions is described. A 'black-box' function is assumed with gradients being unavailable. The use of frames allows gradient estimates to be formed. At each iteration a ray search is performed either along a direct search quasi-Newton direction, or along the ray through the best frame point. The use of randomly oriented frames and random perturbations is examined, the latter yielding a convergence proof on non-smooth
more » ... . Numerical results on non-smooth problems show that the method is effective, and that, in practice, the random perturbations are more important than randomly orienting the frames. The method is applicable to nonlinear 1 and ∞ data fitting problems, and other nonsmooth problems.
doi:10.21914/anziamj.v48i0.95 fatcat:wpuxigkmhfaefol4f4inoy74ry