A modified SQP-filter method and its global convergence

For current sequential programming (SQP) type algorithms, there exist two problems. One is that there are many quadratic programming subproblems are needed to be solved per iteration, the other is that the search direction may be unbounded and caused the sequence to be divergent. In this paper, we presented a modified SQP-filter method based on the modified quadratic subproblem proposed in Zhou [G.L. Zhou, A modified SQP method and its global convergence, J. Global Optim. 11 (1997) 193-205]. This method has no demand on the initial point, and need not using a penalty parameter, which could be problematic to obtain. What is more, the subproblem is feasible at each iterate point. Under some conditions, the global convergence property is obtained.