  Real-time optimization problems are ubiquitous in control and estimation, and
are typically parameterized by incoming measurement data and/or operator
commands. This paper proposes solving parameterized constrained nonlinear
programs using a semismooth predictor-corrector (SSPC) method. Nonlinear
complementarity functions are used to reformulate the first order necessary
conditions of the optimization problem into a parameterized non-smooth
root-finding problem. Starting from an approximate solution, a semismooth
Euler-Newton algorithm is proposed for tracking the trajectory of the
primal-dual solution as the parameter varies over time. Active set changes are
naturally handled by the SSPC method, which only requires the solution of
linear systems of equations. The paper establishes conditions under which the
solution trajectories of the root-finding problem are well behaved and provides
sufficient conditions for ensuring boundedness of the tracking error. Numerical
case studies featuring the application of the SSPC method to nonlinear model
predictive control are reported and demonstrate the advantages of the proposed
method.
