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On the complexity of quadratic programming with two quadratic constraints

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Abstract

The complexity of quadratic programming problems with two quadratic constraints is an open problem. In this paper we show that when one constraint is a ball constraint and the Hessian of the quadratic function defining the other constraint is positive definite, then, under quite general conditions, the problem can be solved in polynomial time in the real-number model of computation through an approach based on the analysis of the dual space of the Lagrange multipliers. However, the degree of the polynomial is rather large, thus making the result mostly of theoretical interest.

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Acknowledgments

The authors are extremely grateful to the Associate Editor and the anonymous reviewers. The comments and critics to previous submissions of our work allowed us to significatively improve the final result.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy

    Luca Consolini & Marco Locatelli

Authors
  1. Luca Consolini
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  2. Marco Locatelli
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Correspondence to Luca Consolini.

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Consolini, L., Locatelli, M. On the complexity of quadratic programming with two quadratic constraints. Math. Program. 164, 91–128 (2017). https://doi.org/10.1007/s10107-016-1073-8

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  • DOI: https://doi.org/10.1007/s10107-016-1073-8

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