A modified SQP method and its global convergence

The sequential quadratic programming method developed by Wilson, Han and Powell may fail if the quadratic programming subproblems become infeasible or if the associated sequence of search directions is unbounded. In [1], Han and Burke give a modification to this method wherein the QP subproblem is altered in a way which guarantees that the associated constraint region is nonempty and for which a robust convergence theory is established. In this paper, we give a modification to the QP subproblem and provide a modified SQP method. Under some conditions, we prove that the algorithm either terminates at a Kuhn-Tucker point within finite steps or generates an infinite sequence whose every cluster is a Kuhn-Tucker point. Finally, we give some numerical examples.