Locally Exact Lower Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

A central problem of branch and bound methods for global optimization is that lower bounds are often not exact even if the diameter of the subdivided regions shrinks to zero This can lead to a large number of subdivisions preventing the method from terminating in reasonable time For the all quadratic optimization problem with convex constraints we present locally exact lower bounds and optimality cuts based on Lagrangian relaxation If all global minimizers ful ll a certain second order optimality condition it can be shown that locally exact lower bounds or optimality cuts lead to nite termination of a branch and bound algorithm Since there exist e cient methods for computing Lagrangian relaxation bounds of all quadratic optimization problems exploiting problem structure our approach should be applicable to large scale structured optimization problems