The security-constrained optimal power flow problem considers both the normal state and contingency constraints, and it is formulated as a large-scale nonconvex optimization problem. We propose a global optimization algorithm based on Lagrangian duality to solve the nonconvex problem to optimality. As usual, the global approach is often time-consuming, thus, for practical uses when dealing with a large number of contingencies, we investigate two decomposition algorithms based on Benders cut and the alternating direction method of multipliers. These decomposition schemes often generate solutions with a smaller objective function values than those generated by the conventional approach and very close to the globally optimal points. © 1969-2012 IEEE.