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Some properties of the lower bound of optimal values in interval convex quadratic programming

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Abstract

One of the fundamental problems in interval quadratic programming is to compute the range of optimal values. In this paper, we derive some results on the lower bound of interval convex quadratic programming. We first develop complementary slackness conditions of a quadratic program and its Dorn dual. Then, some interesting and useful characteristics of the lower bound of interval quadratic programming are established based on these conditions. Finally, illustrative examples and remarks are given to get an insight into the problem discussed.

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Acknowledgements

The authors would like to thank anonymous referees for their comments and suggestions that helped to improve the paper. Especially, Theorem3.4 is enhanced according to one of the reviewers’ suggestion. The authors were partially supported by the NSF of Zhejiang Province (Grant Nos. LY14A010028, Xinmiao2016R407079) and NNSF of China (Grant Nos. 61673145, 11526184, 71471051, U1509217).

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Authors and Affiliations

  1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Wei Li, Jianghong Jin & Mengxue Xia

  2. School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Haohao Li

  3. School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Qi Luo

Authors
  1. Wei Li

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  2. Jianghong Jin

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  3. Mengxue Xia

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  4. Haohao Li

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  5. Qi Luo

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Correspondence toHaohao Li.

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Li, W., Jin, J., Xia, M.et al. Some properties of the lower bound of optimal values in interval convex quadratic programming.Optim Lett11, 1443–1458 (2017). https://doi.org/10.1007/s11590-016-1097-2

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