# Jonathan M. Borwein

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**publisher and metadata sources**).Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex… Continue Reading

and Notation.- Variational Principles.- Variational Techniques in Subdifferential Theory.- Variational Techniques in Convex Analysis.- Variational Techniques and Multifunctions.- Variational… Continue Reading

A broad class of optimization algorithms based on Bregman distances in Banach spaces is unified around the notion of Bregman monotonicity. A systematic investigation of this notion leads to a… Continue Reading

We produce exact cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic-geometric mean iteration of Gauss and Legendre. The iteration in question is $a_n+1 := a_n + 2b_n… Continue Reading

Best entropy estimation is a technique that has been widely applied in many areas of science. It consists of estimating an unknown density from some of its moments by maximizing some measure of the… Continue Reading

Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the… Continue Reading

The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed… Continue Reading

Paper 17: David H. Bailey and Jonathan M. Borwein, “Pi and its friends,” and “Normality: A stubborn question,” from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters,… Continue Reading

We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the… Continue Reading

In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint… Continue Reading