  Nonlinear model predictive control~(NMPC) generally requires the solution of
a non-convex optimization problem at each sampling instant under strict timing
constraints, based on a set of differential equations that can often be stiff
and/or that may include implicit algebraic equations. This paper provides a
local convergence analysis for the recently proposed adjoint-based sequential
quadratic programming~(SQP) algorithm that is based on a block-structured
variant of the two-sided rank-one~(TR1) quasi-Newton update formula to
efficiently compute Jacobian matrix approximations in a sparsity preserving
fashion. A particularly efficient algorithm implementation is proposed in case
an implicit integration scheme is used for discretization of the optimal
control problem, in which matrix factorization and matrix-matrix operations can
be avoided entirely. The convergence analysis results as well as the
computational performance of the proposed optimization algorithm are
illustrated for two simulation case studies of nonlinear MPC.
