A Benders Decomposition Approach for Low Rank Concave Minimization Problems

Abstract

We propose a Benders decomposition approach for an important class of mixed-integer concave minimization problems that is particularly suitable for problems with few concave terms, i.e., low-rank problems. Unlike Generalized Benders decomposition where the nonlinearity is handled at the subproblems, we handle concavity at the master problem and use a unique property of concave minimization to carry out an implicit enumeration. To our knowledge, this approach is the first to tackle concave minimization problems via Benders decomposition. We test and benchmark the proposed approach against state-of-the-art commercial solvers and found it to outperform them in many cases in terms of computational time and/or solution quality.