Geodesic
The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 2A Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : Primary: 90C32, 26B25. 
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     author = {Laura Martein and Laura Carosi},
     title = {The {Sum} of a {Linear} and a {Linear} {Fractional} {Function:} {Pseudoconvexity} on the {Nonnegative} {Orthant} and {Solution} {Methods}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {2A},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_2A_a14/}
}
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Laura Martein; Laura Carosi. The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 2A. http://geodesic.mathdoc.fr/item/BMMS_2012_35_2A_a14/