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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 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 [8]. We find representations of the C n,k in terms of Meijer G-functions and nested-Barnes… (More)

If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. Abstract. In this lecture I shall talk generally about experimental mathematics. Near the end, I briefly present some more detailed and sophisticated examples. Throughout , I emphasize the… (More)

- Heinz H Bauschke, Jonathan M Borwein, Patrick L Combettes, H H Bauschke, J M Borwein, P L Combettes
- 2001

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 and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at… (More)

- H H Bauschke, J M Borwein, A S Lewis
- 1994

The method of cyclic projections is a powerful tool for solving convex feasibility problems in Hilbert space. Although in many applications, in particular in the eld of image reconstruction (electron microscopy, computed tomography), the convex constraint sets do not necessarily intersect, the method of cyclic projections is still employed. Results on the… (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)