Preprint A752/2014
Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function
Alexey F. Izmailov | Mikhail V. Solodov | Evgeniy I. Uskov

An iteration of the stabilized sequential quadratic programming method
  consists in solving a certain quadratic program in the primal-dual space,
  regularized in the dual variables. The advantage with respect to the
  classical sequential quadratic programming is that no constraint qualifications
  are required for fast local convergence (i.e., the problem can be degenerate).
  In particular, for equality-constrained problems the superlinear rate of convergence is
  guaranteed under the only assumption that the primal-dual starting point is close enough to
  a stationary point and a noncritical Lagrange multiplier (the latter being weaker
  than the second-order sufficient optimality condition). However, unlike for
  the usual sequential quadratic programming method, designing natural globally convergent
  algorithms based on the
  stabilized version
  proved quite a challenge and,
  currently, there are very few proposals in this direction. For equality-constrained
  problems, we suggest to use for the task linesearch for the smooth
  two-parameter exact penalty function, which is the sum of the Lagrangian with squared
  penalizations of the violation of the constraints
  and of the violation of  the Lagrangian stationarity with respect to primal variables.
  Reasonable global convergence properties are established.
  Moreover, we show that the globalized algorithm preserves the superlinear rate of
  the stabilized sequential quadratic programming method
  under the weak conditions mentioned above. We also present some numerical
  on a set of degenerate test problems.