Strong Semismoothness of Projection onto Slices of Second-Order Cone

Yingnan Wang () and Naihua Xiu ()
Additional contact information
Yingnan Wang: Beijing Jiaotong University
Naihua Xiu: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 3, No 9, 599-614

Abstract: Abstract Second-order cone (SOC) is a typical subclass of nonpolyhedral symmetric cones and plays a fundamental role in the second-order cone programming. It is already proven that the metric projection mapping onto SOC is strongly semismooth everywhere. However, whether such property holds for each slice of SOC has not been known yet. In this paper, by virtue of a new property of projection onto the closed and convex set with sufficiently smooth boundary, and some new results about projection onto axis-weighted SOC, we give an affirmative answer to this problem. Meanwhile, we also show Clarke’s generalized Jacobian and the directional derivative for the projection mapping onto a slice of SOC.

Keywords: Projection; Strong semismoothness; Manifold; Axis-weighted second-order cone (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-011-9834-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:150:y:2011:i:3:d:10.1007_s10957-011-9834-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-011-9834-2

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().