The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods

The aim of the paper is to present sequential methods for a pseudoconvex optimization problem whose objective function is the sum of a linear and a linear fractional function and the feasible region is a polyhedron, not necessarily compact. Since the sum of a linear and a linear fractional function is not in general pseudoconvex, we first derive conditions characterizing its pseudoconvexity on the nonnegative orthant. We prove that the sum of a linear and a linear fractional function is pseudoconvex if and only if it assumes particular canonical forms. Then, theoretical properties regarding the existence of a minimum point and its location are established, together with necessary and sufficient conditions for the infimum to be finite. The obtained results allow us to suggest simplexlike sequential methods for solving optimization problems having as objective function the proposed canonical forms.