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The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper presents convergence properties of the Nelder–Mead algorithm applied to(More)
How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions. Let A denote the familiar hexagonal lattice shown in Fig. 1. We shall investigate four(More)
Fast, efficient parallel algorithms are presented for discrete event simulations of dynamic channel assignment schemes for wireless cellular communication networks. The driving events are called arrivals and departures, in continuous time, to cells geographically distributed across the service area. A dynamic channel assignment scheme decides which call(More)
We analyze the concurrent-read exclusive-write protocol for access to a shared resource, such as occurs in database and distributed operating systems. Readers arrive according to a Poisson process and acquire shareable i.e., non-exclusive, locks which, once granted, are released after a generally distributed random period. Writers arrive according to an(More)