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Exact two steps SOCP/SDP formulation for a modified conic trust region subproblem

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Abstract

In this paper, we study a modified version of the conic trust region subproblem which arises within a class of nonlinear programming algorithms. First using a variant of S-Lemma, we give an SOCP/SDP formulation which gives its optimal objective value. Then using the parametrization approach of Dinkelbach and the known exact SOCP/SDP relaxation of the extended trust region subproblem, we find its optimal solution. Finally, some preliminary numerical results are given.

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Notes

  1. Second order cone program/Semidefinite program.

  2. Thanks to one of the reviewers who suggested this simplified version of proposition and a short proof.

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Acknowledgments

The author would like to thank suggestions from the three reviewers which substantially improved the current version of the paper and Prof. Wolkowicz for his fruitful discussion on variants of trust region subproblem. The financial support of University of Guilan during author’s sabbatical leave 2015-16, hosted by Prof. Wolkowicz at the Department of Combinatorics and Optimization, University of Waterloo is appreciated.

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

    Maziar Salahi

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  1. Maziar Salahi
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Salahi, M. Exact two steps SOCP/SDP formulation for a modified conic trust region subproblem. Optim Lett 11, 1691–1697 (2017). https://doi.org/10.1007/s11590-016-1080-y

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  • DOI: https://doi.org/10.1007/s11590-016-1080-y

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