The multiple-sets split feasibility problem and its applications for inverse problems

By Yair Censor, T. Elfving, Nirit Kopf, Thomas Bortfeld. 2005

802 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b83f179b6a999e56797d32b6ba08ebfd23e7b33f

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In Computational Theory and Mathematics

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Citations in the corpus

Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem (2011, background): “space, and establish weak convergence for one and strong convergence for the other two.”
Perturbed projections and subgradient projections for the multiple-sets split feasibility problem (2007, methodology): “[14] Given an additional closed convex set Ω ⊆ R n , the constrained multiple-sets split feasibility problem (CMSSFP) is to ﬁnd x ∗ ∈ Ω such that x ∗ solves (1).”
The Split Common Null Point Problem (2011, methodology): “This formulation was used for solving an inverse problem in radiation therapy treatment planning [21, 17].”
An iterative regularization method for the solution of the split feasibility problem in Banach spaces (2008, background): “[21] generalized this procedure to the case where several constraints are imposed in the domain as well as in the range of the linear operator.”
Parallel Extragradient-Proximal Methods for Split Equilibrium Problems (2015, methodology): “A special case of SEP in practice is the split convex feasibility p roblem which had been studied and used as a model in intensity-modulated radiation therap y t eatment planning, see [3,5].”
A unified approach for inversion problems in intensity-modulated radiation therapy (2006, methodology): “The mathematical analysis of the results presented here is included in our companion paper, Censor et al 2005.”
A New Algorithm for Solving The Multiple-Sets Split Feasibility Problem in Banach Spaces (2014, background): “The MSSFP has been widely studied by many authors (see [3, 6, 11, 15, 16, 19, 20, 22, 23]), due to its various real-world applications, such as the inverse problem arising in intensity-modulate radiation therapy [4].”
Applied Iterative Methods (2007, methodology): “The algorithm given in [54] has the iterative step”
Iterative methods for solving the generalized split common null point problem in Hilbert spaces (2020, background): “4, where the coordinates of the centres a1, a2, a3 are randomly generated in [−1, 1], the radii R1,R2,R3 are randomly generated in the intervals [4, 8], [6, 12] and [8, 16], respectively, and the coordinates of the initial point x0 are randomly generated in [−2, 2].”