Integer quadratic optimization

Abstract A branch and bound algorithm is considered to solve linearly constrained, integer quadratic optimization problems. The main result consists in making a rule by which it will be decided in every node of the branch and bound tree which variable is going to branch next such that only a small number of branch and bound nodes need to be investigated. If Fletcher's algorithm is applied to solve continuous partial problems, then only O ( n 2 ) operations are required to find an ‘advantageous’ variable for branching.