A Generalized Approach to Dantzig-Wolfe Decomposition for Concave Programs

The Dantzig-Wolfe decomposition procedure for concave programs can be viewed as inner linearization followed by restriction. This paper presents an approach that allows selective inner linearization of functions and utilizes a generalized pricing problem. It allows considerable flexibility in the choice of functions to be approximated using inner linearization. Use of the generalized pricing problem guarantees that strict improvement in the value of the objective function is achieved at each iteration and provides a termination criterion that is both necessary and sufficient for optimality. A specialization of this procedure results in an algorithm that is a direct extension of the Dantzig-Wolfe decomposition algorithm.