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

Interior point methods in optimal control problems of affine systems: Convergence results and solving algorithms