In this talk we consider two-stage linear adjustable robust optimization problems with continuous and fixed recourse. 

These problems have been the subject of exact solution approaches, notably, constraint generation (CG) and constraint-and-column generation (CCG). 

Both approaches repose on an exponential-sized reformulation of the problem which uses a large number of constraints or constraints and variables.

The decomposition algorithms then solve and reinforce a relaxation of the aforementioned reformulation through the iterations which require the solution of bilinear separation problems. 

Here, we present an alternative approach reposing on a novel reformulation of the problem with an exponential number of semi-infinite constraints. We present a nested decomposition algorithm to deal with the exponential and semi-infinite natures of our formulation separately. 

We argue that our algorithm will lead to a reduced number of bilinear separation problems solved while providing a high quality relaxation.

We perform a detailed numerical study that showcases the superior performance of our proposed approach compared to the state-of-the-art and evaluates the contribution of different algorithmic components.