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Continuity and Directional Differentiability of the Value Function in Parametric Quadratically Constrained Nonconvex Quadratic Programs

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Abstract

The aim of this paper is to investigate the continuity and the directional differentiability of the value function in quadratically constrained nonconvex quadratic programming problem. Our result can be used in some cases where the existing results on differential stability in nonlinear programming (applied to quadratic programming) cannot be used.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.39. The authors would like to thank the anonymous referees for his/her valuable suggestions which have helped to improve the presentation.

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Authors and Affiliations

  1. Hanoi Pedagogical University 2, Hanoi, Vietnam

    Tran Van Nghi & Nguyen Nang Tam

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  1. Tran Van Nghi
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  2. Nguyen Nang Tam
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Correspondence to Tran Van Nghi.

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Van Nghi, T., Tam, N.N. Continuity and Directional Differentiability of the Value Function in Parametric Quadratically Constrained Nonconvex Quadratic Programs. Acta Math Vietnam 42, 311–336 (2017). https://doi.org/10.1007/s40306-016-0179-7

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  • DOI: https://doi.org/10.1007/s40306-016-0179-7

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