(271g) Multi-Level Mixed-Integer Optimization, Adjustable Robust Optimization & Multi-Parametric Programming

We present novel algorithms for the exact, global and parametric solution of two classes of multi-level programming problems, namely (i) bi-level mixed-integer linear or quadratic programming problems (B-MILP or B-MIQP) and (ii) tri-level mixed-integer linear or quadratic programming problems (T-MILP or T-MIQP) containing both integer and continuous variables at all optimization levels. We then demonstrate how these algorithms can be used for the exact and global solution of adjustable robust optimization (ARO) problems – where we propose a novel method for the derivation of generalized affine decision rules for linear/quadratic and mixed-integer linear/quadratic ARO problems. Theoretical advances in multi-parametric programming provide the basis for these developments.