In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantages in different settings of the problem. For each model, we study relevant iterative algorithms, some of which are well-known in this area and some are new. All the studied methods, including the well-known CQ Algorithm, are proven to have global convergence guarantees in the non-convex setting under mild conditions on the problem’s data.

Revised:

Accepted:

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^{1, 2}; Shoham Sabach

^{3}; Sergey Voldman

^{3}

@article{OJMO_2020__1__A1_0, author = {Aviv Gibali and Shoham Sabach and Sergey Voldman}, title = {Non-Convex {Split} {Feasibility} {Problems:} {Models,} {Algorithms} and {Theory}}, journal = {Open Journal of Mathematical Optimization}, eid = {1}, publisher = {Universit\'e de Montpellier}, volume = {1}, year = {2020}, doi = {10.5802/ojmo.1}, language = {en}, url = {https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/} }

TY - JOUR AU - Aviv Gibali AU - Shoham Sabach AU - Sergey Voldman TI - Non-Convex Split Feasibility Problems: Models, Algorithms and Theory JO - Open Journal of Mathematical Optimization PY - 2020 VL - 1 PB - Université de Montpellier UR - https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/ DO - 10.5802/ojmo.1 LA - en ID - OJMO_2020__1__A1_0 ER -

%0 Journal Article %A Aviv Gibali %A Shoham Sabach %A Sergey Voldman %T Non-Convex Split Feasibility Problems: Models, Algorithms and Theory %J Open Journal of Mathematical Optimization %D 2020 %V 1 %I Université de Montpellier %U https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/ %R 10.5802/ojmo.1 %G en %F OJMO_2020__1__A1_0

Aviv Gibali; Shoham Sabach; Sergey Voldman. Non-Convex Split Feasibility Problems: Models, Algorithms and Theory. Open Journal of Mathematical Optimization, Volume 1 (2020), article no. 1, 15 p. doi : 10.5802/ojmo.1. https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/

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