Solution Uniqueness of Convex Optimization Problems via the Radial Cone

Jalal Fadili (), Tran Thai An Nghia () and Duy Nhat Phan ()
Additional contact information
Jalal Fadili: Normandie Université
Tran Thai An Nghia: Oakland University
Duy Nhat Phan: University of Dayton Research Institute

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 19, 32 pages

Abstract: Abstract In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong solution or even a tilt-stable one without checking second-order information. Consequently, we apply our theory to low-rank optimization problems. The radial cone is fully calculated in this case and numerical experiments show that our characterizations are sharp.

Keywords: Solution uniqueness; Convex optimization; Radial cone; Variational analysis and nonsmooth optimization; Nuclear norm minimization problems; 49J52; 49J53; 49K40; 90C25; 90C31 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02723-3 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:206:y:2025:i:2:d:10.1007_s10957-025-02723-3

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

DOI: 10.1007/s10957-025-02723-3

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 ().