A Lagrangian dual method for two-stage robust optimization with binary uncertainties

This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute by solving mixed-integer bilinear subproblems. However, their numerical solution can be computationally expensive not only due resulting large size after reformulating the terms, but also because decision-independent bounds on variables are typically unknown. We propose an alternative Lagrangian dual that circumvents difficulties is readily integrated either algorithm. specialize where binary parameters switch off constraints as commonly encountered applications, discuss extensions lack relatively complete recourse those integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.