Abstract

We discuss the notion of a support collection to a star-shaped set at a certain boundary point and a weak separability of two star-shaped sets. Applications to some problems, including the minimization of a star-shaped distance, are given.

Author information

Contact details are reproduced from the original publication and may be historical.

Evgenii V. Sharikov

CIAO – SITMS, University of Ballarat, P.O. Box 663, Ballarat, Vic. 3353, Australia

Keywords

  • Star-shaped sets
  • separability
  • distance function
  • star-shaped distance
  • best approximation

Mathematics Subject Classification

52A30

References

  1. G. P. Crespi, I. Ginchev, M. Rocca: Existence of solutions and star-shapedness in Minty variational inequalities, J. Glob. Optim, to appear.Google Scholar
  2. A. M. Rubinov: Sublinear operators and their applications, Russ. Math. Surv. 32 (1977) 115–175.https://doi.org/10.1070/RM1977v032n04ABEH001640Google Scholar
  3. A. M. Rubinov: Abstract Convexity and Global Optimization, Kluwer, Dordrecht (2000).https://doi.org/10.1007/978-1-4757-3200-9Google Scholar
  4. A. Shveidel: Separability of star-shaped sets and its application to optimization problems, Optimization 40 (1997) 207–227.https://doi.org/10.1080/02331939708844310Google Scholar
  5. A. Zaffaroni: Is every radiant function the sum of quasiconvex functions?, Math. Methods Oper. Res. 59 (2004) 221–233.https://doi.org/10.1007/s001860300325Google Scholar

Suggested citation

A. M. Rubinov, E. V. Sharikov. “Star-Shaped Separability with Applications.” Journal of Convex Analysis 13 (2006), No. 3/4, 849–860. https://doi.org/10.68381/jca13063

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.