Inexact Cuts in Benders Decomposition

Benders' decomposition is a well-known technique for solving large linear programs with a special structure. In particular it is a popular technique for solving multi-stage stochastic linear programming problems. Early termination in the subproblems generated during Benders' decomposition (assuming dual feasibility) produces valid cuts which are inexact in the sense that they are not as constraining as cuts derived from an exact solution. We describe an inexact cut algorithm, prove its convergence under easily veriiable assumptions, and discuss a corresponding Dantzig-Wolfe decomposition algorithm. The paper is concluded with some computational results from applying the algorithm to a class of stochastic programming problems which arise in hydroelectric scheduling.