  This paper proposes an accelerated version of Feasible Sequential Linear
Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in
all intermediate iterates by means of an iterative update strategy which is
based on repeated evaluation of zero-order information. This technique was
successfully applied to techniques such as Model Predictive Control and Moving
Horizon Estimation, but it can exhibit slow convergence. Moreover, keeping all
iterates feasible in FSLP entails a large number of additional constraint
evaluations. In this paper, Anderson Acceleration (AA($d$)) is applied to the
zero-order update strategy improving the convergence rate and therefore
decreasing the number of constraint evaluations in the inner iterative
procedure of the FSLP algorithm. AA($d$) achieves an improved contraction rate
in the inner iterations, with proven local linear convergence. In addition, it
is observed that due to the improved zero-order update strategy, AA($d$)-FSLP
takes larger steps to find an optimal solution, yielding faster overall
convergence. The performance of AA($d$)-FSLP is examined for a time-optimal
point-to-point motion problem of a parallel SCARA robot. The reduction of the
number of constraint evaluations and overall iterations compared to FSLP is
successfully demonstrated.
