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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 exible framework is(More)
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Like differentiability, convexity is a natural and powerful property of functions that(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. 1 Abstract and Introduction This paper is an extended version of a presentation made at ICME10, related work is elaborated in references [1–7]. 1 I shall generally explore experimental and(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)
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)
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 qualification involving the notion of quasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of(More)