Necessary optimality conditions for optimal control problems with equilibrium constraints

Prof. Jane Ye

May 8, 2015, 8:15 a.m. S3 047

We introduce and study the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with mixed state and control constraints formulated as time dependent complementarity constraints and it can be seen as a dynamic mathematical program with equilibrium constraints (MPEC). It provides a powerful modeling paradigm for many practical problems such as bilevel optimal control problems and dynamic principal-agent problems. In this paper, we propose several Fritz John type stationary conditions for the OCPEC such as the Clarke (C-) stationarity, Mordukhovich (M-) stationarity, and strong (S-) stationarity in line with the C-, M-, and S-stationarities for the MPEC in the literature. Moreover, we give some sufficient conditions to ensure that the local minimizers of the OCPEC are Fritz John type C-, M-, and S-stationary, respectively. This is a joint work with Lei Guo.