On strongly polynomial algorithms for some classes of quadratic programming problems∗†

In this paper we survey some results concerning polynomial and/or strongly polynomial solvability of some classes of quadratic programming problems. The discussion on polynomial solvability of continuous convex quadratic programming is followed by a couple of models for quadratic integer programming which, due to their special structure, allow polynomial (or even strongly polynomial) solvability. The theoretical merit of those results stems from the fact that a running time (i.e. the number of elementary arithmetic operations) of a strongly polynomial algorithm is independent of the input size of the problem.