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Stability for trust-region methods via generalized differentiation

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  • Nguyen Qui

Abstract

We obtain necessary and sufficient conditions for local Lipschitz-like property and sufficient conditions for local metric regularity in Robinson’s sense of Karush–Kuhn–Tucker point set maps of trust-region subproblems in trust-region methods. The main tools being used in our investigation are dual criteria for fundamental properties of implicit multifunctions which are established on the basis of generalized differentiation of normal cone mappings. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:1:p:139-164
    DOI: 10.1007/s10898-013-0086-6
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    References listed on IDEAS

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    1. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.

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