On Projection Algorithms for Solving Convex Feasibility Problems

By Heinz H. Bauschke, Jonathan Michael Borwein. 1996

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Citations in the corpus

Towards neural networks that provably know when they don't know (2019, methodology): “The result is not guaranteed be on the ellipsoid so after the 500 steps we use the alternating projection algorithm (Bauschke & Borwein, 1996) for 10 steps which is guaranteed to converge to a point in the intersection of the ellipsoid and the box because both of these sets are convex.”
The multiple-sets split feasibility problem and its applications for inverse problems (2005, background): “Its values are the radiation intensities at the sources, as a function of source location, that would result in a dose function which agrees with the prescribed dose bounds.”
A projection method for solving nonlinear problems in reflexive Banach spaces (2011, background): “For more information regarding these problems see, for example, [2], [29], [7] and [14], respectively.”
Cyclic algorithms for split feasibility problems in Hilbert spaces (2011, background): “Note that the CFP has received a lot of attention due to its extensive applications in many applied disciplines as diverse as approximation theory, image recovery and signal processing, control theory, biomedical engineering, communications, and geophysics (see [1–3] and the references therein).”
Perturbed projections and subgradient projections for the multiple-sets split feasibility problem (2007, methodology): “The use of such subgradient projections to replace projections onto convex sets in various projection algorithms was done before by several authors, see Censor and Lent [16], Bauschke and Borwein [2, Section 7] and references therein, and Yang [28] for the two-sets-SFP.”
Mixed equilibrium problems and optimization problems (2009, background): “This kind of optimization problems has been studied extensively by many authors, see, for example, Bauschke and Borwein [18], Combettes [19], Deutsch and Yamada [20] and Xu [21] when F̂ = ⋂N i=1 Ci and h(x) = 〈x,b〉.”
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.”
A new proximal point iteration that converges weakly but not in norm (2005, background): “Consequently, (xn)n2N is Fej´er monotone with respect to S. On the other hand, Claim 2 shows that all weak cluster points of (xn)n2N must lie in S. Altogether, by [ 2, Theorem 2.16 ], the sequence (xn)n2N converges weakly to some point in S.”
The asymptotic behavior of the composition of two resolvents (2005, background): “This formulation has found numerous applications in engineering and in the physical sciences; see, for instance, [10,16,19] .”
Self-adaptive algorithms for the split problem of the demicontractive operators (2018, background): “5 [25]: Let be a nonempty closed convex subset inH.”
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory (2017, methodology): “obtain faster convergence. An optimization algorithm utilizing stochastic projection steps was developed in [42]. For a comprehensive survey of projection methods for convex feasibility problems, see [3]. Parallel method. A natural parallelization strategy is to perform one step of the basic method ”