A new double trust regions SQP method without a penalty function or a filter

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.