In this thesis, we study various dynamic pricing problems in the form of infinite-dimensional mathematical programming, i.e., optimal control problems and differential variational inequalities (DVIs), in support of accurate and efficient algorithms. In addition, we describe a method for handling uncertainty in optimal control problems via a robust optimization approach. We provide a formal method for handling uncertainty in the objective function, which may be nonlinear in states, controls, and uncertain parameters.

To develop an algorithm for DVIs, we consider a gap function for DVIs and study an equivalent optimal control problem. In particular, we employ a differential gap function and its gradient to form a descent method for DVIs. To show the descent method is effective, we investigate an application of DVIs to differential Nash games. In particular, we solve an abstract linear-quadratic differential Nash game using our proposed descent method.

We study dynamic pricing problems of three different classes: (1) infrastructure pricing, (2) service pricing, and (3) manufactured good pricing. First, we present a theory of dynamic congestion pricing for vehicular traffic networks; we consider day-to-day as well as within-day time scales in the formulation of a dynamic optimal toll problem with equilibrium constraints. Second, we study a non-cooperative differential game between service providers using a demand learning mechanism. Third, we provide a robust optimal control formulation of a dynamic pricing and inventory control problem in the presence of demand uncertainty.