**Keywords:**

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

experiments

on a set of degenerate test problems.