Circumcentric directions of cones

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 Vol. 17; no. 4; pp. 1069 - 1081
Main Authors: Behling, Roger, Bello-Cruz, Yunier, Lara-Urdaneta, Hugo, Oviedo, Harry, Santos, Luiz-Rafael
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2023
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
65B99
Cone
65K05
90C25
Convex inequality
Feasible direction
49M27
Circumcenter
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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