Name
Abstract | ||
|---|---|---|
The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices included in its definition. This has been established in a previous paper by reducing a QEiCP of dimension n to a special 2n-order EiCP. In this paper we propose an enumerative algorithm for solving the QEiCP by exploiting this equivalence with an EiCP. The algorithm seeks a global minimum of a special Nonlinear Programming Problem (NLP) with a known global optimal value. The algorithm is shown to perform very well in practice but in some cases terminates with only an approximate optimal solution to NLP. Hence, we propose a hybrid method that combines the enumerative method with a fast and local semi-smooth method to overcome the latter drawback. This algorithm is also shown to be useful for computing a positive eigenvalue for an EiCP under similar assumptions. Computational experience is reported to demonstrate the efficacy and efficiency of the hybrid enumerative method for solving the QEiCP. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s11075-015-0064-9 | Numerical Algorithms |
Keywords | Field | DocType |
Eigenvalue problems,Complementarity problems,Nonlinear programming,Global optimization,65F15,90C33,90C30,90C26 | Mathematical optimization,Global optimization,Matrix (mathematics),Mathematical analysis,Nonlinear programming,Quadratic equation,Complementarity theory,Equivalence (measure theory),Mixed complementarity problem,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
72 | 3 | 1017-1398 |
Citations | PageRank | References |
2 | 0.37 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alfredo N. Iusem | 1 | 374 | 62.67 |
| Joaquim J. Judice | 2 | 31 | 1.88 |
| valentina sessa | 3 | 2 | 0.37 |
| Hanif D. Sherali | 4 | 3403 | 318.40 |