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- Heinz H. Bauschke, Jonathan M. Borwein
- SIAM Review
- 1996

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 exible framework is… (More)

- Jonathan M. Borwein, Robert M. Corless
- SIAM Review
- 1996

Historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations Much the same can be said for Euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics More recently we have been forced to consider multidimensional extensions encompassing… (More)

- Jonathan M. Borwein, David M. Bradley, David John Broadhurst
- Electr. J. Comb.
- 1997

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 mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional… (More)

The convex feasibility problem, that is, finding a point in the intersection of finitely many closed convex sets in Euclidean space, arises in various areas of mathematics and physical sciences. It can be solved by the classical method of cyclic orthogonal projections, where, by projecting cyclically onto the sets, a sequence is generated that converges to… (More)

- Heinz H. Bauschke, Jonathan M. Borwein, Wu Li
- Math. Program.
- 1999

The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely 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… (More)

- Jonathan M. Borwein, Adrian S. Lewis
- Math. Program.
- 1992

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)

This paper considers the minimization of a convex integral functional over the positive cone of an Lp space, subject to a finite number of linear equality constraints. Such problems arise in spectral estimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and… (More)

In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov. Consider a polynomial p on R of degree d (the maximum of the degrees of the monomials in the expansion of p). We call p homogeneous if p(tw)… (More)