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A Finitely Convergent Circumcenter Method for the Convex Feasibility Problem

https://doi.org/10.1137/23M1595412

Behling, Roger; Bello-Cruz, Yunier; Iusem, Alfredo N; Liu, Di; Santos, Luiz-Rafael (September 2024, SIAM Journal on Optimization)

In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating halfspaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.
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On the centralization of the circumcentered-reflection method

https://doi.org/10.1007/s10107-023-01978-w

Behling, Roger; Bello-Cruz, Yunier; Iusem, Alfredo N.; Santos, Luiz-Rafael (May 2024, Mathematical Programming)

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Analytical Study and Efficient Evaluation of the Josephus Function

Bello-Cruz, Yunier; Quintero-Contreras, Roy (March 2024, Journal of integer sequences)

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A successive centralized circumcentered-reflection method for the convex feasibility problem

https://doi.org/10.1007/s10589-023-00516-w

Behling, Roger; Bello-Cruz, Yunier; Iusem, Alfredo; Liu, Di; Santos, Luiz-Rafael (January 2024, Computational Optimization and Applications)

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On the Recurrence Formula for Fixed Points of the Josephus Function

https://doi.org/10.5281/zenodo.14547967

Bello-Cruz, Yunier; Quintero-Contreras, Roy (January 2024, Integers)

In this paper, we provide a comprehensive solution to the open problem regarding the existence of a recurrence formula for computing fixed points of the Josephus function precisely when the reduction constant is three. Incorporating this formula into recursive algorithms significantly improves addressing the Josephus problem, particularly for large inputs.
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