Necessary optimality conditions for optimal control problems with equilibrium constraints

Prof. Jane Ye

May 8, 2015, 10:15 a.m. S3 047

We introduce and study the optimal control problem with equilib-
rium 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 math-
ematical 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 prob-
lems. In this paper, we propose several Fritz John type stationary
conditions for the OCPEC such as the Clarke (C-) stationarity, Mor-
dukhovich (M-) stationarity, and strong (S-) stationarity in line with
the C-, M-, and S-stationarities for the MPEC in the literature. More-
over, we give some sufficient conditions to ensure that the local min-
imizers of the OCPEC are Fritz John type C-, M-, and S-stationary,
respectively. This is a joint work with Lei Guo.