On the pseudoconvexity and pseudolinearity of some classes of fractional functions

Abstract

The aim of the article is to study the pseudoconvexity (pseudoconcavity) of the ratio between a quadratic function and the square of an affine function. Applying the Charnes–Cooper transformation of variables the function is transformed in a quadratic one defined on a suitable halfspace. The characterization of the pseudoconvexity of such a quadratic function allows to give necessary and sufficient conditions for the pseudoconvexity and the pseudolinearity of the ratio in terms of the initial data.

Keywords:

• Pseudoconvexity
• Pseudolinearity
• Fractional programming

Keywords:

• Mathematics Subject Classifications 2000: 90C32
• 26B25

Notes

¹ A direct proof of the theorem can be found in 9.