Multi-split Multiple-sets Implicit Convex Feasibility Seeking As Split Inverse Problems
Abstract
We introduce a new class of problems, termed multi-split multiple-sets implicit convex feasibility problems (MSMS-ICFPs), define a proximity function for it and analyze its properties under certain assumptions on the involved general point-to-set operators. Additionally, we discuss its properties for a special class of point-to-set operators. For these kinds of point-to-set operators, we deploy a new iterative algorithm to solve the associated MSMS-ICFP and show that any sequence generated by it converges in norm to a solution of the MSMS-ICFP whenever a solution exists (i.e., in the consistent case). We also define a generalized proximity function for the MSMS-ICFP using the Bregman distance. Based on this function, we present a generalized simultaneous projection gradient algorithm for the split feasibility problem with multiple output sets, by examining various related results. We conclude by discussing several further special cases of the MSMS-ICFP.
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BibTeX
@misc{censor2026multisplit,
title = {{Multi-split Multiple-sets Implicit Convex Feasibility Seeking As Split Inverse Problems}},
author = {Yair Censor and Soumitra Dey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39991},
eprint = {2610.39991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39991},
}
RIS
TY - UNPB
TI - Multi-split Multiple-sets Implicit Convex Feasibility Seeking As Split Inverse Problems
AU - Yair Censor
AU - Soumitra Dey
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39991
UR - https://arxiv.org/abs/2610.39991
AB - We introduce a new class of problems, termed multi-split multiple-sets implicit convex feasibility problems (MSMS-ICFPs), define a proximity function for it and analyze its properties under certain assumptions on the involved general point-to-set operators. Additionally, we discuss its properties for a special class of point-to-set operators. For these kinds of point-to-set operators, we deploy a new iterative algorithm to solve the associated MSMS-ICFP and show that any sequence generated by it converges in norm to a solution of the MSMS-ICFP whenever a solution exists (i.e., in the consistent case). We also define a generalized proximity function for the MSMS-ICFP using the Bregman distance. Based on this function, we present a generalized simultaneous projection gradient algorithm for the split feasibility problem with multiple output sets, by examining various related results. We conclude by discussing several further special cases of the MSMS-ICFP.
ER -