A Branch and Bound algorithm for solving nonconvex minimization problem based on reducing duality gap

In this paper, we derive a general principle demonstrating that partitioning the feasible set, the duality gap, existing between a nonconvex program and its lagrangian dual, can be reduced. The principle can be implemented in a Branch and Bound algorithm which computes an approximate global solution and a corresponding lower bound on the global optimal value. The algorithm involves decomposition and a local search. Numerical results with an example for applying algorithm are given.