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
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.