  This paper presents an interior point method for pure-state and
mixed-constrained optimal control problems for dynamics, mixed constraints, and
cost function all affine in the control variable. This method relies on
resolving a sequence of two-point boundary value problems of differential and
algebraic equations. This paper establishes a convergence result for primal and
dual variables of the optimal control problem. A primal and a primal-dual
solving algorithm are presented, and a challenging numerical example is treated
for illustration. Accepted for publication at SIAM SICON 2023
