  In this paper we consider a nonconvex optimization problem with nonlinear
equality constraints. We assume that both, the objective function and the
functional constraints, are locally smooth. For solving this problem, we
propose a linearized quadratic penalty method, i.e., we linearize the objective
function and the functional constraints in the penalty formulation at the
current iterate and add a quadratic regularization, thus yielding a subproblem
that is easy to solve, and whose solution is the next iterate. Under a dynamic
regularization parameter choice, we derive convergence guarantees for the
iterates of our method to an $\epsilon$ first-order optimal solution in
$\mathcal{O}(1/{\epsilon^3})$ outer iterations. Finally, we show that when the
problem data satisfy Kurdyka-Lojasiewicz property, e.g., are semialgebraic, the
whole sequence generated by our algorithm converges and we derive convergence
rates. We validate the theory and the performance of the proposed algorithm by
numerically comparing it with the existing methods from the literature.
