Deterministic algorithms for constrained concave minimization: A unified critical survey

The purpose of this article is to present a unified critical survey of the deterministic solution algorithms for constrained concave minimization. To unify and streamline the survey, the article first describes four fundamental techniques that serve as building blocks for most of these algorithms. These four techniques are extreme point ranking, concavity cut reduction, outer approximation, and branch and bound. Using these descriptions, the article then surveys the deterministic algorithms for constrained concave minimization by grouping them into three categories of approaches. These categories are enumeration, successive approximation, and successive partitioning. This strategy provides a means of efficiently conveying the essential mechanics and the relative strengths and weaknesses of most of the well-known concave minimization algorithms.