Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty

Abstract In this paper a class of robust two-stage combinatorial optimization problems is discussed. It assumed that the uncertain second-stage costs are specified in form convex uncertainty set, particular polyhedral or ellipsoidal ones. shown versions basic network and selection NP-hard, even very restrictive cases. Some exact approximation algorithms for general problem constructed. Polynomial problems, such as shortest path also provided.