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Exact SDP Reformulations for Adjustable Robust Quadratic Optimization with Affine Decision Rules

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Abstract

In this paper, we deal with exact semidefinite programming (SDP) reformulations for a class of adjustable robust quadratic optimization problems with affine decision rules. By virtue of a special semidefinite representation of the non-negativity of separable non-convex quadratic functions on box uncertain sets, we establish an exact SDP reformulation for this adjustable robust quadratic optimization problem on spectrahedral uncertain sets. Note that the spectrahedral uncertain set contains commonly used uncertain sets, such as ellipsoids, polytopes, and boxes. As special cases, we also establish exact SDP reformulations for this adjustable robust quadratic optimization problems when the uncertain sets are ellipsoids, polytopes, and boxes, respectively. As applications, we establish the corresponding results for fractionally adjustable robust quadratic optimization problems.

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Funding

This research is supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZDK202100803), the Team Building Project for Graduate Tutors in Chongqing (yds223010) and the Innovation Project of CTBU (yjscxx2023-211-72).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Huan Zhang & Xiangkai Sun

  2. School of Mathematical Sciences, Sunway University, 47500, Bandar Sunway, Selangor Darul Ehsan, Malaysia

    Kok Lay Teo

Authors
  1. Huan Zhang
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  2. Xiangkai Sun
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  3. Kok Lay Teo
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Correspondence to Xiangkai Sun.

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Communicated by Jen-Chih Yao.

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Zhang, H., Sun, X. & Teo, K.L. Exact SDP Reformulations for Adjustable Robust Quadratic Optimization with Affine Decision Rules. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-023-02371-5

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  • DOI: https://doi.org/10.1007/s10957-023-02371-5

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