Journal of Global Optimization

, Volume 52, Issue 4, pp 797–829

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


    • Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong Kong
  • X. L. Sun
    • Department of Management Science, School of ManagementFudan University
  • C. L. Liu
    • Department of Applied MathematicsShanghai University of Finance and Economics

DOI: 10.1007/s10898-011-9713-2

Cite this article as:
Li, D., Sun, X.L. & Liu, C.L. J Glob Optim (2012) 52: 797. doi:10.1007/s10898-011-9713-2


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.


Quadratic 0–1 programmingNonlinear integer programmingOptimality conditionLower boundsVariable fixationBranch-and-bound method

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© Springer Science+Business Media, LLC. 2011