Sequential quadratic programming (SQP) methods are a popular class of methods for the solution of nonlinear optimization problems. They are particularly effective for solving a sequence of related problems, such as those arising in mixed-integer nonlinear programming and the optimization of functions subject to differential equation constraints. Recently, there has been considerable interest in the formulation of stabilized SQP methods, which are specifically designed to give rapid convergence on degenerate problems. Existing stabilized SQP methods are essentially local, in the sense that both the formulation and analysis focus on a neighborhood of an optimal solution. In this talk we discuss an SQP method that has favorable global convergence properties yet is equivalent to a conventional stabilized SQP method in the neighborhood of a solution.