García-Palomares, U. M.; Rodríguez, J. F. New sequential and parallel derivative-free algorithms for unconstrained minimization. (English) Zbl 1049.90133 SIAM J. Optim. 13, No. 1, 79-96 (2002). Summary: This paper presents sequential and parallel derivative-free algorithms for finding a local minimum of smooth and nonsmooth functions of practical interest. It is proved that, under mild assumptions, a sufficient decrease condition holds for a nonsmooth function. Based on this property, the algorithms explore a set of search directions and move to a point with a sufficiently lower functional value. If the function is strictly differentiable at its limit points, a (sub)sequence of points generated by the algorithm converges to a first-order stationary point (\(\nabla f(x) = 0\)). If the function is convex around its limit points, convergence (of a subsequence) to a point with nonnegative directional derivatives on a set of search directions is ensured. Preliminary numerical results on sequential algorithms show that they compare favorably with the recently introduced pattern search methods. Cited in 18 Documents MSC: 90C56 Derivative-free methods and methods using generalized derivatives 65K10 Numerical optimization and variational techniques Keywords:nonsmooth function; unconstrained minimization; derivative-free algorithm; parallel algorithms; necessary and sufficient conditions Software:KELLEY; DFO; fminsearch PDFBibTeX XMLCite \textit{U. M. García-Palomares} and \textit{J. F. Rodríguez}, SIAM J. Optim. 13, No. 1, 79--96 (2002; Zbl 1049.90133) Full Text: DOI