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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
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…
On Projection Algorithms for Solving Convex Feasibility Problems
A very broad and flexible framework is investigated which allows a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence in convex feasibility problems.
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
A framework which allows to circumvent the intricate question of Lipschitz continuity of gradients by using an elegant and easy to check convexity condition which captures the geometry of the constraints is introduced.
The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space
- Heinz H. Bauschke
- 15 August 1996
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,…
SIAM Journal on Optimization
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…
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
A simple modification of iterative methods arising in numerical mathematics and optimization that makes them strongly convergent without additional assumptions is presented.
Legendre functions and the method of random Bregman projections
The convex feasibility problem, that is, nding a point in the intersection of nitely many closed convex sets in Euclidean space, arises in various areas of mathematics and physical sciences. It can…
Bregman Monotone Optimization Algorithms
A systematic investigation of the notion of Bregman monotonicity leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate BRegman projection schemes.
On the convergence of von Neumann's alternating projection algorithm for two sets
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…
Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization
It is shown that the standard constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull intersection property.