Cone asymptotes of convex sets
DOI:
https://doi.org/10.17398/2605-5686.36.1.81Palabras clave:
Plane asymptote, cone asymptote, convex setResumen
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
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.