Article

Journal of Global Optimization

, Volume 52, Issue 4, pp 797-829

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

  • D. LiAffiliated withDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong Kong Email author 
  • , X. L. SunAffiliated withDepartment of Management Science, School of Management, Fudan University
  • , C. L. LiuAffiliated withDepartment of Applied Mathematics, Shanghai University of Finance and Economics

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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.

Keywords

Quadratic 0–1 programming Nonlinear integer programming Optimality condition Lower bounds Variable fixation Branch-and-bound method