Dual bounds and optimality cuts for all-quadratic programs with convex constraints (Q5929999)

For the all-quadratic optimization problem with convex constraints optimality cuts are introduced which cut off a given local minimizer from the feasible set. A branch-and-bound algorithm is proposed that uses optimality cuts which are finite if all global minimizers satisfy a certain second order condition. The optimality cuts are based on a dual problem with additional redundant conditions. This technique is also used to derive tight lower bounds as well as to construct dual bounds for certain problems with zero duality gap.