Constraint-Based Lagrangian Relaxation

This paper studies how to generalize Lagrangian relaxation to high-level optimization models, including constraint-programming and local search models. It exploits the concepts of constraint violation (typically used in constraint programming and local search) and constraint satisfiability (typically exploited in mathematical programming). The paper considers dual and primal methods, studies their properties, and discusses how they can be implemented in terms of high-level model combinators and algorithmic templates. Experimental results suggest the potential benefits of Lagrangian methods for improving high-level constraint programming and local search models.