On a Robust Approach to “split” Feasibility Problems: Solvability and Global Error Bound Conditions
本文研究一类凸可行性问题的鲁棒方法，利用凸分析和变分分析技术，将鲁棒分裂可行性问题转化为集值包含形式，从而借助可解性与稳定性理论，给出了解存在性和误差界的充分条件，并通过例子讨论，特别关注多面体情形下的误差界条件。
Abstract In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds are investigated. This is done by reformulating the robust counterpart of a split feasibility problem as a set-valued inclusion, a problem format for which one can take profit from the solvability and stability theory that has been recently developed. As a result, a sufficient condition for solution existence and error bounds is established in terms of problem data and discussed through several examples. A specific focus is devoted to error bound conditions in the case in which the robust counterpart of split feasibility problems is polyhedral. Connections with some of the existent error bound conditions for the original split feasibility problem are also discussed.