Name
Abstract | ||
|---|---|---|
In this paper, the solution of the symmetric quadratic eigenvalue complementarity problem QEiCP is addressed. The QEiCP has a solution provided the so-called co-regular and co-hyperbolic properties hold and is said to be symmetric if all the matrices involved in its definition are symmetric. We show that under the two conditions stated above the symmetric QEiCP can be reduced to the problem of computing a stationary point of an appropriate nonlinear program NLP. We also investigate the reduction of the QEiCP to a simpler eigenvalue complementarity problem EiCP. This transformation enables us to show that the co-regular and co-hyperbolic properties are not necessary for the existence of a solution to the QEiCP. Furthermore the QEiCP is shown to be equivalent to the problem of finding a stationary point of a quadratic fractional program QFP under special conditions on the matrices of the QEiCP. The use of the so-called spectral projected-gradient SPG algorithm for dealing with the programs NLP and QFP is also investigated. Some considerations about the implementation of this algorithm are discussed. Computational experience is included to highlight the efficiency of the algorithm for finding a solution of the QEiCP by exploring the NLPs mentioned above. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1080/10556788.2013.854359 | Optimization Methods and Software |
Keywords | Field | DocType |
problem qeicp,co-hyperbolic property,so-called co-regular,quadratic fractional program qfp,simpler eigenvalue complementarity problem,programs nlp,appropriate nonlinear program,symmetric quadratic eigenvalue complementarity,symmetric qeicp,stationary point,global optimization,nonlinear programming | Mathematical optimization,Matrix (mathematics),Nonlinear programming,Complementarity theory,Stationary point,Linear complementarity problem,Divide-and-conquer eigenvalue algorithm,Mixed complementarity problem,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
29 | 4 | 1055-6788 |
Citations | PageRank | References |
7 | 0.50 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luís M. Fernandes | 1 | 35 | 2.83 |
| Joaquim J. Júdice | 2 | 126 | 10.30 |
| Masao Fukushima | 3 | 34 | 5.07 |
| Alfredo Iusem | 4 | 14 | 2.24 |