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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
Proximal Splitting Methods in Signal Processing
TLDR
The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework.
Signal Recovery by Proximal Forward-Backward Splitting
We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation
Equilibrium programming in Hilbert spaces
Several methods for solving systems of equilibrium problems in Hilbert spaces – and for finding best approximations thereof – are presented and their convergence properties are established. The
The foundations of set theoretic estimation
TLDR
A single formal framework is presented to synthesize various approaches to set theory estimation, and the fundamental philosophy, goals, and analytical techniques of set theoretic estimation are discussed.
The foundations of set theoretic estimation
TLDR
A single formal framework is presented to synthesize various approaches to set theory estimation, and the fundamental philosophy, goals, and analytical techniques of set theoretic estimation are discussed.
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
TLDR
A simple modification of iterative methods arising in numerical mathematics and optimization that makes them strongly convergent without additional assumptions is presented.
Bregman Monotone Optimization Algorithms
TLDR
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.
A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
TLDR
A decomposition method based on the Douglas-Rachford algorithm for monotone operator-splitting for signal recovery problems and applications to non-Gaussian image denoising in a tight frame are demonstrated.
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