A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problem

Carmo P. Brás, Andreas Fischer, Joaquim J. Júdice, Klaus Schönefeld, Sarah Seifert

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we address the solution of the symmetric eigenvalue complementarity problem (EiCP) by treating an equivalent reformulation of finding a stationary point of a fractional quadratic program on the unit simplex. The spectral projected-gradient (SPG) method has been recommended to this optimization problem when the dimension of the symmetric EiCP is large and the accuracy of the solution is not a very important issue. We suggest a new algorithm which combines elements from the SPG method and the block active set method, where the latter was originally designed for box constrained quadratic programs. In the new algorithm the projection onto the unit simplex in the SPG method is replaced by the much cheaper projection onto a box. This can be of particular advantage for large and sparse symmetric EiCPs. Global convergence to a solution of the symmetric EiCP is established. Computational experience with medium and large symmetric EiCPs is reported to illustrate the efficacy and efficiency of the new algorithm. (C) 2016 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)36-48
Number of pages13
JournalApplied Mathematics and Computation
Volume294
Publication statusPublished - 1 Feb 2017

Keywords

  • Complementarity problems
  • Eigenvalue problems
  • Nonlinear programming
  • Large-scale optimization

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