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An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach

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Abstract

We explore in this paper certain rich geometric properties hidden behind quadratic 0–1 programming. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0–1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0–1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results.

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Authors and Affiliations

  1. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    D. Li

  2. Department of Management Science, School of Management, Fudan University, Shanghai, 200433, People’s Republic of China

    X. L. Sun

  3. Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    C. L. Liu

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  1. D. Li
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  2. X. L. Sun
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  3. C. L. Liu
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Correspondence to D. Li.

Additional information

This work was supported by Research Grants Council of Hong Kong Grants CUHK4245/04E and 413606, by National Natural Science Foundation of China Grants 10971034 and 70832002, and by the Joint NSFC/RGC Grant 71061160506.

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Li, D., Sun, X.L. & Liu, C.L. An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach. J Glob Optim 52, 797–829 (2012). https://doi.org/10.1007/s10898-011-9713-2

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  • DOI: https://doi.org/10.1007/s10898-011-9713-2

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