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Copositivity and constrained fractional quadratic problems

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Abstract

We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Applications of the CFQP and StFQP, related with the correction of infeasible linear systems and eigenvalue complementarity problems are also discussed.

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Acknowledgments

The authors are indebted to two anonymous referees and an anonymous Associate Editor for valuable remarks which led to several improvements of a previous version; for instance, Subsect. 2.2 was added upon the suggestions of a referee.

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Authors and Affiliations

  1. DM, Universidade Nova de Lisboa, Lisbon, Portugal

    Paula Amaral

  2. ISOR, University of Vienna, Vienna, Austria

    Immanuel M. Bomze

  3. DM, Universidade de Coimbra and Instituto de Telecomunicações, Coimbra, Portugal

    Joaquim Júdice

Authors
  1. Paula Amaral
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  2. Immanuel M. Bomze
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  3. Joaquim Júdice
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Correspondence to Immanuel M. Bomze.

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Amaral, P., Bomze, I.M. & Júdice, J. Copositivity and constrained fractional quadratic problems. Math. Program. 146, 325–350 (2014). https://doi.org/10.1007/s10107-013-0690-8

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