Characterizations of strictly convex sets by the uniqueness of support points

Ha TXD, Jahn J (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Optimization Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

Book Volume: 68

Pages Range: 1321-1335

Journal Issue: 7

DOI: 10.1080/02331934.2018.1476513

Abstract

This short paper characterizes strictly convex sets by the uniqueness of support points (such points are called unique support points or exposed points) under appropriate assumptions. A class of so-called regular sets, for which every extreme point is a unique support point, is introduced. Closed strictly convex sets and their intersections with some other sets are shown to belong to this class. The obtained characterizations are then applied to set-valued maps and to the separation of a convex set and a strictly convex set. Under suitable assumptions, so-called set-valued maps with path property are characterized by strictly convex images of the considered set-valued map.

Authors with CRIS profile

Johannes Jahn Naturwissenschaftliche Fakultät

Involved external institutions

Hanoi Institute of Mathematics VN Viet Nam (VN)

How to cite

APA:

Ha, T.X.D., & Jahn, J. (2019). Characterizations of strictly convex sets by the uniqueness of support points. Optimization, 68(7), 1321-1335. https://dx.doi.org/10.1080/02331934.2018.1476513

MLA:

Ha, Truong Xuan Duc, and Johannes Jahn. "Characterizations of strictly convex sets by the uniqueness of support points." Optimization 68.7 (2019): 1321-1335.

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