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Checking weak and strong optimality of the solution to interval convex quadratic programming in a general form

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Abstract

We discuss the problems of checking weak and strong optimality of the solution to interval convex quadratic programs in a general form. A given vector is called a weakly(strongly) optimal solution to an interval convex quadratic program if it is an optimal solution for some(each) concrete setting of the interval convex quadratic program. Based on the feature of feasible directions, different methods to test weak and strong optimality of a given vector corresponding to general interval convex quadratic programs, including both equations and inequalities, are proposed respectively, as well as some useful corollaries. Several numerical examples are given to show the effectiveness of the main results.

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Acknowledgements

The authors would like to thank anonymous referees for their comments and suggestions that helped to improve the paper, and Min Wang for participating in the discussion at the beginning of this research. This work was supported by the Natural Science Foundation of Zhejiang Province (Grant No. LY21A010021).

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Authors and Affiliations

  1. Department of Mathematics, PLA Army Academy of Artillery and Air Defense, Hefei, 230031, China

    Mengxue Xia & Daojun Xu

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

    Haohao Li

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  1. Mengxue Xia
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Correspondence to Haohao Li.

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Xia, M., Li, H. & Xu, D. Checking weak and strong optimality of the solution to interval convex quadratic programming in a general form. Optim Lett 18, 339–364 (2024). https://doi.org/10.1007/s11590-023-01998-7

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