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Stability for trust-region methods via generalized differentiation

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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.

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Authors and Affiliations

  1. College of Information and Communication Technology, Can Tho University, 1 Ly Tu Trong, Can Tho, Vietnam

    Nguyen Thanh Qui

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  1. Nguyen Thanh Qui
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Correspondence to Nguyen Thanh Qui.

Additional information

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2011.01. The author thanks the anonymous referees very much for their valuable remarks and suggestions that have improved the paper.

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Qui, N.T. Stability for trust-region methods via generalized differentiation. J Glob Optim 59, 139–164 (2014). https://doi.org/10.1007/s10898-013-0086-6

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  • DOI: https://doi.org/10.1007/s10898-013-0086-6

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