Solution of Fractional Quadratic Programs on the Simplex and Application to the Eigenvalue Complementarity Problem

Joaquim Júdice (), Valentina Sessa and Masao Fukushima
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Joaquim Júdice: FCTUC - DEEC Polo II Universidade de Coimbra
Valentina Sessa: PSL Research University
Masao Fukushima: The Kyoto College of Graduate Studies for Informatics

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 24, 545-573

Abstract: Abstract In this paper, we introduce an implementation of Dinkelbach’s algorithm for computing a global maximum of a fractional linear quadratic program (FLQP) on the simplex that employs an efficient block principal pivoting algorithm in each iteration. A new sequential FLQP algorithm is introduced for computing a stationary point (SP) of a fractional quadratic program (FQP) on the simplex. Global convergence for this algorithm is established. This sequential algorithm is recommended for the solution of the symmetric eigenvalue complementarity problem (EiCP), as this problem is equivalent to the computation of an SP of an FQP on the simplex. Computational experience reported in this paper indicates that the implementation of Dinkelbach’s method for the FLQP and the sequential FLQP algorithm are quite efficient in practice. An extension of the sequential FLQP algorithm for solving the nonsymmetric EiCP is also introduced. Since this method solves a special variational inequality (VI) problem in each iteration, it can be considered as a sequential VI algorithm. Although the convergence of this algorithm has yet to be established, preliminary computational experience indicates that the sequential VI algorithm is quite a promising technique for the solution of the nonsymmetric EiCP.

Keywords: Fractional quadratic programming; Quadratic programming; Eigenvalue problems; Complementarity problems; 90C26; 90C32; 90C33; 90C30; 93B60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02019-w

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