  In this paper, we propose a method that has foundations in the line search
sequential quadratic programming paradigm for solving general nonlinear
equality constrained optimization problems. The method employs a carefully
designed modified line search strategy that utilizes second-order information
of both the objective and constraint functions, as required, to mitigate the
Maratos effect. Contrary to classical line search sequential quadratic
programming methods, our proposed method is endowed with global convergence and
local superlinear convergence guarantees. Moreover, we extend the method and
analysis to the setting in which the constraint functions are deterministic but
the objective function is stochastic or can be represented as a finite-sum. We
also design and implement a practical inexact matrix-free variant of the
method. Finally, numerical results illustrate the efficiency and efficacy of
the method.
