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

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.