The Optimal Value Function is Lipschitz Continuous Convex Optimization

• Published: 10 March 2015

Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs

Applied Mathematics-A Journal of Chinese Universities volume 30,pages 102–110 (2015)Cite this article

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Abstract

When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.

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Author information

Authors and Affiliations

1. School of Science, Xi'an Polytechnic University, Xi'an, 710048, China

   You-pan Han

2. Department of Computing Science, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

   Zhi-ping Chen & Feng Zhang

Corresponding author

Correspondence to Zhi-ping Chen.

Additional information

Supported by the National Natural Science Foundation of China (10571141, 70971109, 71371152), the first author is also supported by the Talents Fund of Xi'an Polytechnic University (BS1320) and the Mathematics Discipline Development Fund of Xi'an Ploytechnic University (107090701).

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Han, Yp., Chen, Zp. & Zhang, F. Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs. Appl. Math. J. Chin. Univ. 30, 102–110 (2015). https://doi.org/10.1007/s11766-015-3124-y

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• Received: 08 October 2012

• Published: 10 March 2015

• Issue Date: March 2015

• DOI : https://doi.org/10.1007/s11766-015-3124-y

MR Subject Classification

• 90C20

Keywords

• quadratic program
• Lipschitz continuity
• value function
• feasible solution
• KKT solution set

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