A new double trust regions SQP method without a penalty function or a filter (Q712469)

A new double trust regions sequential quadratic programming method (SQP) for solving equality constrained optimization is presented. Each trial step is computed using a double trust regions strategy in two phases, the first of which aims feasibility and the second, optimality. Thus, the approach is similar to inexact restoration methods for nonlinear programming. The most important feature of this paper is to prove global convergence to first-order critical points under some reasonable assumptions without using a penalty function or a filter. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of \textit{N. I. M. Gould} and \textit{P. L. Toint} [Math. Program. 122, No. 1 (A), 155--196 (2010; Zbl 1216.90069); erratum ibid. 131, No. 1--2(A), 403--404 (2012)]. Numerical results demonstrate the efficiency of this new approach.