Circumcentric directions of cones

Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide inward directions to sets given by convex inequalities. In partic...

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Bibliographic Details
Published in:Optimization letters 2023-05, Vol.17 (4), p.1069-1081
Main Authors: Behling, Roger, Bello-Cruz, Yunier, Lara-Urdaneta, Hugo, Oviedo, Harry, Santos, Luiz-Rafael
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
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Summary:Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide inward directions to sets given by convex inequalities. In particular, we show that circumcentric directions of finitely generated cones belong to the interior of their polars. We also derive a measure of interiorness of the circumcentric direction, which then provides a special cone of search directions, all being feasible to the convex region under consideration.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-022-01923-4