Cone asymptotes of convex sets

Autores/as

  • V. Soltan Department of Mathematical Sciences, George Mason University 4400 University Drive, Fairfax, VA 22030, USA

DOI:

https://doi.org/10.17398/2605-5686.36.1.81

Palabras clave:

Plane asymptote, cone asymptote, convex set

Resumen

Based on the notion of plane asymptote, we introduce the new concept of cone asymptote of a set in the n-dimensional Euclidean space. We discuss the existence and describe some families of cone asymptotes.

Descargas

Los datos de descarga aún no están disponibles.

Referencias

A. Auslender, M. Teboulle, “Asymptotic Cones and Functions in Optimization and Variational Inequalities”, Springer-Verlag, New York, 2003.

D. Gale, V. Klee, Continuous convex sets, Math. Scand. 7 (1959), 379 – 391.

P. Goossens, Hyperbolic sets and asymptotes, J. Math. Anal. Appl. 116 (1986), 604 – 618.

V. Klee, Asymptotes and projections of convex sets, Math. Scand. 8 (1960), 356 – 362.

V.L. Klee, Asymptotes of convex bodies, Math. Scand. 20 (1967), 89 – 90.

J. Lawrence, V. Soltan, On unions and intersections of nested families of cones, Beitr. Algebra Geom. 57 (2016), 655 – 665.

J.E. Martı́nez-Legaz, D. Noll, W. Sosa, Minimization of quadratic functions on convex sets without asymptotes, J. Convex Anal. 25 (2018), 623 – 641.

J.E. Martı́nez-Legaz, D. Noll, W. Sosa, Non-polyhedral extensions of the Frank and Wolfe theorem, in “Splitting Algorithms, Modern Operator Theory, and Applications” (H. Bauschke, R. Burachik, D. Luke editors), Springer, Cham, 2019, 309 – 329.

V. Soltan, Asymptotic planes and closedness conditions for linear images and vector sums of sets, J. Convex Anal. 25 (2018), 1183 – 1196.

V. Soltan, “Lectures on Convex Sets”, Second edition, World Scientific, Hackensack, NJ, 2020.

V. Soltan, On M-decomposable sets, J. Math. Anal. Appl. 485 (2020), 123816, 15 pp.

Descargas

Publicado

2021-06-20

Número

Sección

Convex Geometry

Cómo citar

Cone asymptotes of convex sets. (2021). Extracta Mathematicae, 36(1), 81-98. https://doi.org/10.17398/2605-5686.36.1.81