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Behavior of DCA sequences for solving the trust-region subproblem

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Abstract

From our results it follows that any DCA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476–505, 1998) is convergent provided that the basic matrix of the problem is nonsingular and it does not have multiple negative eigenvalues. Besides, under this additional assumption, there exists such an open set Ω containing the global minimizers and the unique local-nonglobal minimizer (if such exists) that any DCA sequence with the initial point from Ω is contained in the set and converges to a global minimizer or the local-nonglobal minimizer. Various examples are given to illustrate the limiting behavior and stability of the DCA sequences. Structure of the KKT point set of the trust-region subproblem is also analyzed.

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Authors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science (LITA), Paul Verlaine University of Metz, Ile du Saulcy, 57045, Metz Cedex, France

    Hoai An Le Thi

  2. Laboratory of Modelling, Optimization and Operations Research (LMI), National Institute for Applied Sciences (INSA) - Rouen, BP08-Avenue de l’Université, 76801, Saint-Etienne-du-Rouvray, France

    Tao Pham Dinh

  3. Vietnamese Academy of Science and Technology, Institute of Mathematics, Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

    Nguyen Dong Yen

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  1. Hoai An Le Thi
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  2. Tao Pham Dinh
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  3. Nguyen Dong Yen
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Correspondence to Hoai An Le Thi.

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Le Thi, H.A., Pham Dinh, T. & Yen, N.D. Behavior of DCA sequences for solving the trust-region subproblem. J Glob Optim 53, 317–329 (2012). https://doi.org/10.1007/s10898-011-9696-z

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  • DOI: https://doi.org/10.1007/s10898-011-9696-z

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