Journal of Global Optimization

, Volume 52, Issue 4, pp 797–829 | Cite as

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

Article

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 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong
  2. 2.Department of Management Science, School of ManagementFudan UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Applied MathematicsShanghai University of Finance and EconomicsShanghaiPeople’s Republic of China

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