A projective quasi-Newton method for nonlinear optimization

AbstractA trust region method for nonlinear optimization problems with equality constraints is proposed in this paper. This method incorporates quadratic subproblems in which orthogonal projective matrices of the Jacobian of constraint functions are used to replace QR decompositions. As QR decomposition does not ensure continuity, but projective matrix does, convergence behaviour of the new method can be discussed under more reasonable assumptions. The method maintains a two-step feature: one movement in the range space of the Jacobian, whereas the other one in the null space. It is proved that all accumulation points of iterates are KKT (Karush-Kuhn-Tucker) points and the method has a one-step superlinear convergence rate