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 feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is… (More)
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 simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate Bregman projection schemes. Another key… (More)
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 notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for… (More)
The strong conical hull intersection property and bounded linear regularity are properties of a collection of nitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that… (More)
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum eld theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the eld. Here, we assemble results for Euler/Zagier sums (also known as multidimensional… (More)
We apply experimental-mathematical principles to analyze integrals C n,k := 1 n! ∞ 0 · · · ∞ 0 dx 1 dx 2 · · · dx n (cosh x 1 + · · · + cosh x n) k+1. These are generalizations of a previous integral C n := C n,1 relevant to the Ising theory of solid-state physics . We find representations of the C n,k in terms of Meijer G-functions and nested-Barnes… (More)
Let a beavector of real numbers. By an integer relation for a we mean a non-zero integer vector c such that ca T = 0. W e discuss the algorithms for nding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.