Computational Optimization and Applications

, Volume 51, Issue 3, pp 1119–1135 | Cite as

Reconstructing a matrix from a partial sampling of Pareto eigenvalues

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Abstract

Let Λ={λ1,…,λp} be a given set of distinct real numbers. This work deals with the problem of constructing a real matrix A of order n such that each element of Λ is a Pareto eigenvalue of A, that is to say, for all k∈{1,…,p} the complementarity system
$$x\geq \mathbf{0}_n,\quad Ax-\lambda_k x\geq \mathbf{0}_n,\quad \langle x, Ax-\lambda_k x\rangle = 0$$
admits a nonzero solution x∈ℝn.

Keywords

Cone-constrained eigenvalue problem Pareto spectrum Inverse Pareto eigenvalue problem Newton method Normal flow algorithm Underdetermined system of equations 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Department of MathematicsUniversity of AvignonAvignonFrance

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