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The symmetric eigenvalue complementarity problem

Authors: Marcelo Queiroz, Joaquim Júdice and Carlos Humes, Jr.
Journal: Math. Comp. 73 (2004), 1849-1863
MSC (2000): Primary 90C33, 47A75; Secondary 90C30, 82B05
Published electronically: August 20, 2003
MathSciNet review: 2059739
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Abstract: In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.

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Additional Information

Marcelo Queiroz
Affiliation: Computer Science Department, University of São Paulo, Rua do Matão 1010, 05508-090 São Paulo, SP, Brazil

Joaquim Júdice
Affiliation: Mathematics Department, University of Coimbra, 3000 Coimbra, Portugal

Carlos Humes, Jr.
Affiliation: Computer Science Department, University of São Paulo, Rua do Matão 1010, 05508-090 São Paulo, SP, Brazil

Received by editor(s): March 26, 2002
Received by editor(s) in revised form: January 23, 2003
Published electronically: August 20, 2003
Additional Notes: The first author was supported by FAPESP Grant Nos. 97/06227-2 and 02/01351-7.
The second author was supported by FCT project POCTI/35059/MAT/2000.
Article copyright: © Copyright 2003 American Mathematical Society