On the interplay between interior point approximation and parametric sensitivities in optimal control

Infinite-dimensional parameter-dependent optimization problems of the form ‘minJ(u;p) subject to g(u)⩾0’ are studied, where u is sought in an L∞ function space, J is a quadratic objective functional, and g represents pointwise linear constraints. This setting covers in particular control constrained optimal control problems. Sensitivities with respect to the parameter p of both, optimal solutions of the original problem, and of its approximation by the classical primal-dual interior point approach are considered. The convergence of the latter to the former is shown as the homotopy parameter μ goes to zero, and error bounds in various Lq norms are derived. Several numerical examples illustrate the results.