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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)

We consider schemes for reuse-eecient packet access in wireless data networks. We show that computing the maximum ergodic packet arrival rate is NP-hard. We give an upper bound on the maximum er-godic throughput in terms of the eigenvalues of matrices related to the path-gain matrix. We present simple, practical heuristic algorithms which exhibit good… (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)