min-max-min

On the Convergence of Column-and-Constraint Generation Algorithms in Two-Stage Robust Optimization

Categories Robust Optimization Tags , , , , , , ,

We study the well-posedness and convergence of column-and-constraint generation algorithms for general two-stage robust optimization problems. The analysis is formulated in terms of regularity properties of the objective, the second-stage feasible region mapping, and the separation value function, without relying on a particular algebraic representation of the second-stage problem. We give sufficient conditions for the … Read more

Approximation Algorithms for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

Categories Approximation Algorithms, Robust Optimization Tags , , ,

In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It … Read more

New complexity results and algorithms for min-max-min robust combinatorial optimization

Categories Combinatorial Optimization, Convex and Nonsmooth Optimization, Robust Optimization Tags , , ,

In this work we investigate the min-max-min robust optimization problem applied to combinatorial problems with uncertain cost-vectors which are contained in a convex uncertainty set. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions would … Read more