The foundations of set theoretic estimation

By Patrick L. Combettes, M. Civanlar. 1991

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

The Ideal Continual Learner: An Agent That Never Forgets (2023, methodology): “The formulation of Combettes (1993) can be described as follows.”
Proximal Splitting Methods in Signal Processing (2009, methodology): “One of the first widely used convex optimization splitting al orithms in signal processing is POCS (Projection Onto Convex Sets) [31, 42, 141].”
Full length article: The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle (2014, unknown): “, [5], [15], and [16]) — as such, a plethora of algorithms based on the nearest point mappings (projectors) PU and PV have been proposed to solve it.”
The Adaptive Projected Subgradient Method over the Fixed Point Set of Strongly Attracting Nonexpansive Mappings (2006, unknown): “P.L. Combettes (1997).”
Applied Iterative Methods (2007, background): “This point of view is increasingly important in applications such as medical imaging and a number of recent papers have addressed the theoretical and practical issues involved [9], [11], [8], [40], [44], [50], [64], [65], [67].”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “In the above example, C can be thought of as a set of signals possessing a certain property (see [21, 23, 29, 67, 74] for examples of closed convex sets modeling pertinent constraints in signal recovery).”
A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery (2007, methodology): “POCS has been used in scores of signal processing problems [15], [17], [47] and has been extended to more flexible projection algorithms [16], [18] that have found further applications, e.”
Alternating Proximal Algorithms for Weakly Coupled Minimization Problems. Applications to Dynamical Games and PDE’s (2008, background): “(2) This type of variational problem occurs in various domains such as decision sciences and game theory [4], partial differential equations and mechanics [2], optimal control and approximation theory [13], image processing and signal theory [7, 11].”
Adaptive Projected Subgradient Method for Asymptotic Minimization of Sequence of Nonnegative Convex Functions (2005, background): “…and Webb, 1982) to the convex feasibility problem (Bauschke and Borwein, 1996; Bregman, 1965; Butnariu and Mehrez, 1992; Censor and Zenios, 1997; Combettes, 1993, 1997; Gubin et al., 1967; Pierra, 1984; Yamada, 2001; Yamada et al., 2002b; Youla and Webb, 1982), for finding a point (or an…”