Preface: decomposition methods for hard optimization problems

Abstract

Divide and conquer, from Latin divide et impera, is one of the key techniques for tackling combinatorial optimization problems. It relies on the idea of decomposing complex problems into a sequence of subproblems that are then easier to handle. Decomposition techniques (such as Dantzig-Wolfe, Lagrangian, or Benders decomposition) are extremely effective in a wide range of applications, including cutting and packing, production and scheduling, routing and logistics, telecommunications, transportation, and many others. Moreover, decomposition techniques play an important role in many different fields of mixed-integer linear and non-linear optimization, multi objective optimization, optimization under uncertainty, bilevel optimization, etc. Despite the tremendous amount of research on these topics, the mathematical optimization community is constantly faced with new challenges coming from theoretical aspects and real world applications that require the development of new advanced tools.