[users at ionimaging] Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

[Yair Censor]

Dear Colleagues,
We are pleased to announce the availability of our new paper which has just
been published Open Access online.
Title, URL, and Abstract are given below and the EarlyView PDF is attached.
Best regards and Happy New Year!
Mark, Aviv and Yair.

M. Brooke, Y. Censor and A. Gibali, "Dynamic string-averaging CQ-methods
for the split feasibility problem with percentage violation constraints
arising in radiation therapy treatment planning", *International
Transactions in Operational Research* (2020). Published online: December
30, 2020. Available at
https://onlinelibrary.wiley.com/doi/full/10.1111/itor.12929.

*Abstract*.
We study a feasibility-seeking problem with percentage violation
constraints (PVCs). These are additional
constraints that are appended to an existing family of constraints, which
single out certain subsets of the
existing constraints and declare that up to a specified fraction of the
number of constraints in each subset is
allowed to be violated by up to a specified percentage of the existing
bounds. Our motivation to investigate
problems with PVCs comes from the field of radiation therapy treatment
planning (RTTP) wherein the fully
discretized inverse planning problem is formulated as a split feasibility
problem and the PVCs give rise to
nonconvex constraints. Following the CQ algorithm of Byrne (2002, Inverse
Problems, Vol. 18, pp. 441–53),
we develop a string-averaging CQ-method that uses only projections onto the
individual sets that are halfspaces
represented by linear inequalities. The question of extending our
theoretical results to the nonconvex sets
case is still open. We describe how our results apply to RTTP and provide a
numerical example.

Prof. Yair Censor, Dept. of Mathematics, Univ. of Haifa, Mt. Carmel, Haifa
3498838, Israel. Homepage: http://math.haifa.ac.il/yair.
To learn more about the superiorization methodology go to:
https://en.wikipedia.org/wiki/Superiorization and to:
http://math.haifa.ac.il/yair/bib-superiorization-censor.html#top
<http://math.haifa.ac.il/YAIR/bib-superiorization-censor.html#top>.
"Science is the solution of problems whose exact formulations are known
only after they are solved".
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