A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem

Masao Fukushima, Joaquim Júdice, Welington Oliveira and Valentina Sessa ()
Additional contact information
Masao Fukushima: Nanzan University
Joaquim Júdice: Universidade de Coimbra
Welington Oliveira: PSL Research University, CMA Centre de Mathématiques Appliquées
Valentina Sessa: PSL Research University, CMA Centre de Mathématiques Appliquées

Computational Optimization and Applications, 2020, vol. 77, issue 3, No 5, 728 pages

Abstract: Abstract In this paper, we introduce a Sequential Partial Linearization (SPL) algorithm for finding a solution of the symmetric Eigenvalue Complementarity Problem (EiCP). The algorithm can also be used for the computation of a stationary point of a standard fractional quadratic program. A first version of the SPL algorithm employs a line search technique and possesses global convergence to a solution of the EiCP under a simple condition related to the minimum eigenvalue of one of the matrices of the problem. Furthermore, it is shown that this condition is verified for a simpler version of the SPL algorithm that does not require a line search technique. The main computational effort of the SPL algorithm is the solution of a strictly convex standard quadratic problem, which is efficiently solved by a finitely convergent block principal pivoting algorithm. Numerical results of the solution of test problems from different sources indicate that the SPL algorithm is in general efficient for the solution of the symmetric EiCP in terms of the number of iterations, accuracy of the solution and total computational effort.

Keywords: Complementarity problems; Eigenvalue problems; Fractional quadratic programming; Quadratic programming; MSC 90C26; MSC 90C32; MSC 90C33; MSC 90C30; MSC 93B60 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00226-7 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:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00226-7

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-020-00226-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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