Global convergence of a robust filter SQP algorithm

We present a robust filter SQP algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming proposed by Burke to avoid the infeasibility of the quadratic programming subproblem at each iteration. Compared with other filter SQP algorithms, our algorithm does not require any restoration phase procedure which may spend a large amount of computation. The main advantage of our algorithm is that it is globally convergent without requiring strong constraint qualifications, such as Mangasarian–Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). Furthermore, the feasible limit points of the sequence generated by our algorithm are proven to be the KKT points if some weaker conditions are satisfied. Numerical results are also presented to show the efficiency of the algorithm.