An algebra-based approach for linearly constrained concave minimization

This paper proposes an algebra approach for solving the linearly constrained continuous quasi-concave minimization problems. The study involves a class of very generalized concave functions, continuous strictly quasi-concave functions. Based on the fact that the optimal solutions can be achieved at an extreme point of the polyhedron, we provide an algebra-based method for identifying the extreme points. The case on unbounded polyhedral constraints is also discussed and solved. Numerical examples are provided for illustration.