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 simplex- like sequential methods for solving optimization problems having as objective function the proposed canonical forms.

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

MARTEIN, LAURA;CAROSI, LAURA
2012

Abstract

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 simplex- like sequential methods for solving optimization problems having as objective function the proposed canonical forms.
Martein, Laura; Carosi, Laura
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/205431
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