A new trust-region SQP method for equality constrained optimization is considered. This method avoids using a penalty function or a filter, and yet can be globally convergent to first-order critical points under some reasonable assumptions. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of Gould and Toint [Math. Program., 122 (2010), pp. 155-196]. Numerical results demonstrate that this new approach is potentially useful. Mathematical subject classification: 65K05, 90C30, 90C55.

In this paper we present a filter sequential quadratic programming (SQP) algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming (QP) subproblem proposed by Burke and Han, and it can avoid the infeasibility of the QP 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. We underline that global convergence is derived without assuming any constraint qualifications. Preliminary numerical results are reported.