  We revisit and adapt the extended sequential quadratic method (ESQM) in [3]
for solving a class of difference-of-convex optimization problems whose
constraints are defined as the intersection of level sets of Lipschitz
differentiable functions and a simple compact convex set. Particularly, for
this class of problems, we develop a variant of ESQM, called ESQM with
extrapolation (ESQM$_e$), which incorporates Nesterov's extrapolation
techniques for empirical acceleration. Under standard constraint
qualifications, we show that the sequence generated by ESQM$_e$ clusters at a
critical point if the extrapolation parameters are uniformly bounded above by a
certain threshold. Convergence of the whole sequence and the convergence rate
are established by assuming Kurdyka-Lojasiewicz (KL) property of a suitable
potential function and imposing additional differentiability assumptions on the
objective and constraint functions. In addition, when the objective and
constraint functions are all convex, we show that linear convergence can be
established if a certain exact penalty function is known to be a KL function
with exponent $\frac12$; we also discuss how the KL exponent of such an exact
penalty function can be deduced from that of the original extended objective
(i.e., sum of the objective and the indicator function of the constraint set).
Finally, we perform numerical experiments to demonstrate the empirical
acceleration of ESQM$_{e}$ over a basic version of ESQM, and illustrate its
effectiveness by comparing with the natural competing algorithm SCP$_{ls}$ from
[35].
