On Sufficiency in Multiobjective Fractional Programming Problems

The purpose of this paper is to study a class of nondifferentiable multiobjective fractional programming problems with inequality constraints. After a deep investigation on the invex functions, a new kind of generalized invexity, namely (b, alpha) - rho - (eta, theta)-invexity, (b, alpha) - rho - (eta, theta)-pseudoinvexity, and (b, alpha) - rho - (eta, theta)-quasiinvexity, are firstly defined where the functions involved are locally Lipschitz by means of the concepts of generalized Clarke directional derivative and generalized subgradient. Several known invex functions can be deduced as special cases. And an important property, which the ratio of (b, alpha) - rho - (eta, theta)-invex functions is also (b, alpha) - rho - (eta, theta)-invex, is proved. In addition, by utilizing the assumptions of various new generalized invex functions and the above property, several sufficient optimality conditions are obtained and proved for a feasible solution to be an efficient solution or a weakly efficient solution for the multiobjective fractional programming problem involving nonsmooth Lipschitz functions. The results extend and improve the corresponding results in the literature.