Multistage robust mixed-integer optimization under endogenous uncertainty

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In robust optimization context, however, it rarely been considered. This work addresses multistage mixed-integer with decision-dependent sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect set. We derive a tractable reformulation of problem by leveraging recent advances construction nonlinear decision rules, introduce discontinuous piecewise linear rules for recourse. Computational experiments are performed gain insights on impact endogenous uncertainty, benefit discrete computational performance. Our results indicate level conservatism solution can be significantly reduced if properly modeled.