Solving a generalization of the p-regularized subproblems by matrix simultaneous diagonalization via congruence

Nguyen Van-Bong ()
Additional contact information
Nguyen Van-Bong: Tay Nguyen University

Journal of Global Optimization, 2025, vol. 93, issue 2, No 7, 523-534

Abstract: Abstract We are concerned with solving a generalization of the p-regularized subproblems (denoted by (Gp-RS) for short). On one hand, the (Gp-RS) with nonsingular regularized term is the main ingredient of the regularization methods for unconstrained problems and has been studied intensively. On the other hand, (Gp-RS) itself arises in many practical applications and in those cases its regularized term may be singular so that it may have no optimal solutions. It is interesting that if the matrices in the quadratic term and in the regularized term are not simultaneously diagonalizable via congruence (SDC), the (Gp-RS) can only be unbounded from below. If those two matrices are SDC, the (Gp-RS) can be reformulated into one of three cases: an unbounded problem, a p-regularized subproblem (p-RS) of smaller size, or a sum of a (p-RS) of smaller size and an unconstrained quadratic problem with separable variables.

Keywords: Simultaneous diagonalization via congruence; Trust region subproblem; Generalized trust region subproblem; p-regularized subproblems; Positive semidefinite interval; Matrix pencil; 90C20; 90C26; 15A18; 15A22; 15A23 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-025-01536-y 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:jglopt:v:93:y:2025:i:2:d:10.1007_s10898-025-01536-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-025-01536-y

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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