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Trust region subproblem with an additional linear inequality constraint

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Abstract

This paper studies an extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with a single linear inequality constraint. We present an efficient algorithm to solve the problem using a diagonalization scheme that requires solving a simple convex minimization problem. Attainment of the global optimality conditions is discussed. Our preliminary numerical experiments on several randomly generated test problems show that, the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large scale problems.

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Acknowledgments

The authors would like to thank the reviewer for the helpful comments on the early version of this paper.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    M. Salahi

  2. Department of Mathematics, Salman Farsi University of Kazerun, Kazerun, Iran

    S. Fallahi

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  1. M. Salahi
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  2. S. Fallahi
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Correspondence to M. Salahi.

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Salahi, M., Fallahi, S. Trust region subproblem with an additional linear inequality constraint. Optim Lett 10, 821–832 (2016). https://doi.org/10.1007/s11590-015-0957-5

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  • DOI: https://doi.org/10.1007/s11590-015-0957-5

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