A robust choice of the Lagrange multipliers in the successive quadratic programming method

We study the choice of the Lagrange multipliers in the successive quadratic programming method (SQP) applied to the equality constrained optimization problem.; It is known that the augmented Lagrangian SQP-Newton method depends on the penalty parameter only through the multiplier in the Hessian matrix of the Lagrangian function. This effectively reduces the augmented Lagrangian SQP-Newton method to the Lagrangian SQP Newton method where only the multiplier estimate depends on the penalty parameter. In this work, we construct a multiplier estimate that depends strongly on the penalty parameter and we derive a choice for the penalty parameter so that the Hessian matrix, restricted to the null space of the constraints, is positive definite and well conditioned. We demonstrate that the SQP-Newton method with this choice of Lagrange multipliers is locally and q-quadratically convergent.