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A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem

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Abstract

In this paper, we introduce a Sequential Partial Linearization (SPL) algorithm for finding a solution of the symmetric Eigenvalue Complementarity Problem (EiCP). The algorithm can also be used for the computation of a stationary point of a standard fractional quadratic program. A first version of the SPL algorithm employs a line search technique and possesses global convergence to a solution of the EiCP under a simple condition related to the minimum eigenvalue of one of the matrices of the problem. Furthermore, it is shown that this condition is verified for a simpler version of the SPL algorithm that does not require a line search technique. The main computational effort of the SPL algorithm is the solution of a strictly convex standard quadratic problem, which is efficiently solved by a finitely convergent block principal pivoting algorithm. Numerical results of the solution of test problems from different sources indicate that the SPL algorithm is in general efficient for the solution of the symmetric EiCP in terms of the number of iterations, accuracy of the solution and total computational effort.

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Authors and Affiliations

  1. Faculty of Science and Technology, Nanzan University, Nagoya, Japan

    Masao Fukushima

  2. Instituto de Telecomunicações, Universidade de Coimbra, Coimbra, Portugal

    Joaquim Júdice

  3. MINES ParisTech, PSL Research University, CMA Centre de Mathématiques Appliquées, CS 10207 - 1, rue Claude Daunesse, 06904, Sophia Antipolis Cedex, France

    Welington de Oliveira & Valentina Sessa

Authors
  1. Masao Fukushima
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  2. Joaquim Júdice
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  3. Welington de Oliveira
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  4. Valentina Sessa
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Correspondence to Valentina Sessa.

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The research of J. Júdice is funded by FCT/MCTES through national funds and when applicable co-funded EU funds under the project UIDB/EEA/50008/2020.

W. de Oliveira acknowledges financial support from the Gaspard-Monge program for Optimization and Operations Research (PGMO) Project “Models for planning energy investment under uncertainty”.

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Fukushima, M., Júdice, J., de Oliveira, W. et al. A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem. Comput Optim Appl 77, 711–728 (2020). https://doi.org/10.1007/s10589-020-00226-7

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  • DOI: https://doi.org/10.1007/s10589-020-00226-7

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