We introduce a new concept of efficiency in vector optimization. This concept, super efficiency, is shown to have many desirable properties. In particular, we show that in reasonable settings the super efficient points of a set are norm-dense in the efficient frontier. We also provide a Chebyshev characterization of super efficient points for nonconvex sets… (More)
This article gives a brief history of the analysis and computation of the mathematical constant = 3:14159 : : :, including a number of the formulas that have been used to compute through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of to over six billion decimal digits using high-order… (More)
We survey and enhance salient parts of the literature about difference convex functions with specific regard to current knowledge and applications of DC functions.
We analyse the behaviour of the newly introduced cyclic Douglas–Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty.
SPECT (Single Photon Emission Computed Tomography) techniques have been applied to a wide range of medical studies. The stability of a SPECT model depends strongly upon the data collected. We show that a SPECT model is full rank and well-conditioned (stable) if the projection data are large enough. Condition number estimates for a linear model are given.… (More)
In the first of these two lectures I shall talk generally about experimental mathematics. In Part II, I shall present some more detailed and sophisticated examples. The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multi-processor) computers and the pervasive presence of the internet allow… (More)
The problem of function reconstruction from a small number of accurate moments is reviewed and studied numerically. Since this problem is underdetermined, a number of selections have been proposed to pick out a single function. We consider those selections of the \entropic" variety, i.e. those of the form f(x) = Z (x(t))dt for some convex function. We… (More)
The desire to understand π, the challenge, and originally the need, to calculate ever more accurate values of π, the ratio of the circumference of a circle to its diameter, has challenged mathematicians–great and less great—for many many centuries. Recently, π has provided compelling examples of computational mathematics. It is also part of both… (More)