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This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is… Expand

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… Expand

A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications

The proximal gradient and its variants is one of the most attractive first-order algorithm for minimizing the sum of two convex functions, with one being nonsmooth. However, it requires the… Expand

Determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for finding common fixed points of nonexpansive mappings in Hilbert space,… Expand

The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear… Expand

We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present… Expand

We give several unifying results, interpretations, and examples regarding the convergence of the von Neumann alternating projection algorithm for two arbitrary closed convex nonempty subsets of a… Expand

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… Expand

We analyze Dykstra?s algorithm for two arbitrary closed convex sets in a Hilbert space. Our technique also applies to von Neumann?s algorithm. Various convergence results follow. An example allows… Expand

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… Expand