  Nonlinear Programs (NLPs) are prevalent in optimization-based control of
nonlinear systems. Solving general NLPs is computationally expensive,
necessitating the development of fast hardware or tractable suboptimal
approximations. This paper investigates the sensitivity of the solutions of
NLPs with polytopic constraints when the nonlinear continuous objective
function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging
perturbation analysis using a convex modulus, we derive guaranteed bounds on
the distance between the optimal solution of the original
polytopically-constrained NLP and that of its approximated formulation. Our
approach aids in determining criteria for achieving desired solution bounds.
Two case studies on the Eggholder function and nonlinear model predictive
control of an inverted pendulum demonstrate the theoretical results.
