A Non-Interior-Point Continuation Method for the Optimal Control Problem with Equilibrium Constraints

Author name not available (Why is that?)

Publication date: 19 October 2022

Abstract: In this study, we propose a numerical solution method for the optimal control problem with equilibrium constraints (OCPEC). OCPEC can be discretized into a perturbed finite-dimensional nonlinear programming (NLP) problem and further relaxed to satisfy the fundamental constraint qualifications. Therefore, its solution can be obtained by the continuation method that solves a sequence of well-posed NLP problems. However, numerical difficulties that the interior of the feasible region shrinks toward the disjunctive and empty set, arise when the perturbed parameter is close to zero. Hence, we propose a dedicated NLP solver that maps the Karush--Kuhn--Tucker conditions into a system of equations, referred to as the non-interior-point (NIP) method. Compared with active-set methods, the NIP method considers all inequality constraints at each iteration, which is similar to the interior-point (IP) method and suitable for large-scale problems. However, it does not enforce all iterates to remain in the feasible interior, leading to a larger stepsize to mitigate the geometrical difficulties of the feasible region. Moreover, we introduce some numerical techniques to improve the solver performance. The local convergence and solution error are analyzed under certain assumptions. Comparisons with an off-the-shelf IP solver demonstrate that the proposed method is capable of finding a better solution, less sensitive to the ill-posedness of the feasible region, and requires significantly fewer iterations.

Has companion code repository: https://github.com/ky-lin22/nipocpec

This page was built for publication: A Non-Interior-Point Continuation Method for the Optimal Control Problem with Equilibrium Constraints

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6414408)