  In this paper we deal with stochastic optimization problems where the data
distributions change in response to the decision variables. Traditionally, the
study of optimization problems with decision-dependent distributions has
assumed either the absence of constraints or fixed constraints. This work
considers a more general setting where the constraints can also dynamically
adjust in response to changes in the decision variables. Specifically, we
consider linear constraints and analyze the effect of decision-dependent
distributions in both the objective function and constraints. Firstly, we
establish a sufficient condition for the existence of a constrained equilibrium
point, at which the distributions remain invariant under retraining. Morevoer,
we propose and analyze two algorithms: repeated constrained optimization and
repeated dual ascent. For each algorithm, we provide sufficient conditions for
convergence to the constrained equilibrium point. Furthermore, we explore the
relationship between the equilibrium point and the optimal point for the
constrained decision-dependent optimization problem. Notably, our results
encompass previous findings as special cases when the constraints remain fixed.
To show the effectiveness of our theoretical analysis, we provide numerical
experiments on both a market problem and a dynamic pricing problem for parking
based on real-world data.
