Semi-infinite Multiobjective Fractional Programming I

Abstract

In this chapter, we first present three new classes of generalized convex functions involving Hadamard directional derivatives, namely, (strictly) ($\mathcal {F},$ $\beta ,$ $\phi ,$ $\rho ,$ $\eta ,$ $\theta ,$ $\mu$)-Hd-univex functions, (strictly) ($\mathcal {F},$ $\beta ,$ $\phi ,$ $\rho ,$ $\eta ,$ $\theta ,$ $\mu$)-Hd-pseudounivex functions, and (prestrictly) ($\mathcal {F},$ $\beta ,$ $\phi ,$ $\rho ,$ $\eta ,$ $\theta ,$ $\mu$)-Hd-quasiunivex functions, and then, using these functions, we examine numerous sets of sufficient efficiency conditions for a semi-infinite multiobjective fractional programming problem with infinitely many equality and inequality constraints defined on a normed linear space. These results are crucial to further research endeavors.