A projected indefinite dogleg path method for equality constrained optimization (Q1307246)

The authors propose a 2-step trust region indefinite dogleg path method for the solution of nonlinear equality constrained optimization problems. The method is a globally convergent modification of the locally convergent method of \textit{R. Fontecilla} [SIAM J. Numer. Anal. 25, No. 3, 692-712 (1988; Zbl 0698.65042)] and an indefinite dogleg path method is proposed to get approximate solutions of quadratic programming subproblems even if the Hessian in the model is indefinite. The dogleg paths lie in the null space of the Jacobian matrix of the constraints. An \(\ell_1\) exact penalty function is used in the method to determine if a trial point is accepted. The global convergence and the local two-step superlinear convergence rate are proved. Some numerical results are presented.