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

Authors:
D. Li;X. L. Sun;C. L. Liu
Affiliations:
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of China 200433
Venue:
Journal of Global Optimization
Year:
2012

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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.